Section 2.5: Prime Factorization and the Least Common Multiple
Find the prime factorization of 441 using the ladder method. Provide your answer below:
3⋅3⋅7⋅7 3^2⋅7^2 Divide the number by the smallest prime, which is 3. 1473441 Continue dividing by 3 until it no longer divides evenly. 4931473441 Divide by the next prime, 7. 774931473441 The quotient, 7, is prime so the ladder is complete and we can write the prime factorization of 441 as 3⋅3⋅7⋅7 3^2⋅7^2
Identify the number 1843 as either prime or composite. Select the correct answer below: Prime Composite
Composite Test each prime, in order, to see if it is a factor of 1843, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 1843?2Last digit is not 0, 2, 4, 6, or 8.No.31+8+4+3=16 and 16 is not divisible by 3.No.5The last digit is not 5 or 0.No.71843÷7=263.286...No.111843÷11=167.545...No.131843÷13=141.769...No.171843÷17=108.412...No.191843÷19=97Yes. Since 1843 is divisible by 19 we know it is not prime. It is composite.
Example Question: Find the prime factorization of 120 using the ladder method.
Solution: Divide the number by the smallest prime, which is 2. 602120 Continue dividing by 2 until it no longer divides evenly. 152302602120 Divide by the next prime, 3. 53152302602120 The quotient, 5, is prime, so the ladder is complete. Write the prime factorization of 120. 2⋅2⋅2⋅3⋅5 2^3⋅3⋅5 Check this yourself by multiplying the factors. The result should be 120.
Find all the factors of 64.(Use commas to separate the factors.) Provide your answer below:
1, 2, 4, 8, 16, 32 and 64. Divide 64 by each of the counting numbers starting with 1. If the quotient is a whole number, the divisor and quotient are a pair of factors. DividendDivisorQuotientFactors641641, 64642322, 32643∼21.333-644164, 1664512.8-646∼10.667-647∼9.143-64888, 8 In the next line, the quotient would be smaller than the divisor, so we stop. If we continued, we would end up only listing the same factors again in reverse order. Listing all the factors from smallest to greatest, we have 1,2,4,8,16,32, and 64.
Find all the factors of 265.(Use commas to separate the factors.) Provide your answer below:
1,5,53,265 Divide 265 by each of the counting numbers starting with 1. If the quotient is a whole number, the divisor and quotient are a pair of factors. DividendDivisorQuotientFactors 265 1 265 1, 265 265 2 132.5 - 265 3 ∼88.333 - 265 4 66.25 - 2655535, 532656∼44.167 - 265 7 ∼37.857 - 265833.125-2659∼29.444-2651026.5-26511∼24.091-26512∼22.083-26513∼20.385-26514∼18.929-26515∼17.667-26516∼16.563- In the next line, the quotient would be smaller than the divisor, so we stop. If we continued, we would end up only listing the same factors again in reverse order. Listing all the factors from smallest to greatest, we have 1,5,53, and 265.
Identify the number as prime or composite: 137.
137 is prime. Test each prime, in order, to see if it is a factor of 137, starting with 2 as shown. We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 137?2Last digit of 137 is not 0,2,4,6, or 8.No.31+3+7=11, and 11 is not divisible by 3.No.5The last digit of 137 is not 5 or 0.No.7137÷7=19.5714...No.11137÷11=12.454545...No.13137÷13=10.538...No. We can stop when we get to 13 because the quotient (10.538...) is less than the divisor. We did not find any prime numbers that are factors of 137, so we know 137 is prime.
Find the prime factorization of 48 using the ladder method.
2 × 2 × 2 × 2 × 3 Divide the number by the smallest prime, 2. 24248 Continue dividing by 2 until it no longer divides evenly. 326212224248 The quotient, 3, is prime, so the ladder is complete. Write the prime factorization of 48. 2⋅2⋅2⋅2⋅3 2^4⋅3
Find the prime factorization of 48 using the ladder method. Provide your answer below:
2 × 2 × 2 × 2 × 3. Divide the number by the smallest prime, 2. 24248 Continue dividing by 2 until it no longer divides evenly. 326212224248 The quotient, 3, is prime, so the ladder is complete. Write the prime factorization of 48. 2⋅2⋅2⋅2⋅3 2^4⋅3
Find the prime factorization of 1036 using the ladder method. Provide your answer below:
2 × 2 × 7 × 37 2 × 2 × 7 × 37
Find the prime factorization of 1362 using a factor tree. Use the multiplication sign, ×, instead of the letter x to separate the factors. It can be found on the keyboard provided below. Provide your answer below:
2 × 3 × 227. prime factor tree for 1362 is shown below. The figure shows a factor tree for the number 1362.Two branches descend from 1362 and terminate at 2 and 681 respectively. Since 2 is prime it is circled.Two more branches descend from 681 and terminate at 3 and 227 respectively, which are both prime and therefore circled. Note that your factor tree may look different if you started with a different pair of factors, but the circled primes you end up with should be the same.The prime factorization of 1362 is given by the product of the circled primes 2⋅3⋅227
Identify the number 257 as either prime or composite. Select the correct answer below: Prime Composite
257 is prime. Test each prime, in order, to see if it is a factor of 257, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 257?2Last digit is not 0, 2, 4, 6, or 8.No.32+5+7=14 and 14 is not divisible by 3.No.5The last digit is not 5 or 0.No.7257÷7=36.714...No.11257÷11=23.364...No.13257÷13=19.769...No.17257÷17=15.118...No. We can stop before we get to the next prime, 17, because the quotient will be less than the divisor. We did not find any prime numbers that are factors of 257 so we know 257 is prime.
Find the prime factorization of 1412 using the ladder method.
2^2⋅353 Divide the number by the smallest prime, which is 2. 70621412 Continue dividing by 2 until it no longer divides evenly. 353270621412 The quotient, 353, is prime so the ladder is complete and we can write the prime factorization of 1412 as 2⋅2⋅353 2^2⋅353
Find the prime factorization of 1716 using the ladder method. Provide your answer below:
2^2⋅3⋅11⋅13 Divide the number by the smallest prime, which is 2. 85821716 Continue dividing by 2 until it no longer divides evenly. 429285821716 Divide by the next prime, 3. 1433429285821716 Divide by the next prime, 11. 13111433429285821716 The quotient, 13, is prime so the ladder is complete and we can write the prime factorization of 1716 as 2^⋅2⋅3⋅11⋅1322⋅3⋅11⋅13
Find the prime factorization of 580 using the ladder method.
2^2⋅5⋅29 Divide the number by the smallest prime, which is 2. 2902580 Continue dividing by 2 until it no longer divides evenly.14522902580Divide by the next prime, 5.29514522902580The quotient, 29, is prime so the ladder is complete and we can write the prime factorization of 580 as2⋅2⋅5⋅2922⋅5⋅29
Find the prime factorization of 232 using the ladder method.
2times 2times 2times 29
Find the prime factorization of 120 using the ladder method. Do NOT write an equation; just write the expression. Provide your answer below:
2×2×2×3×5 2^3×3×5
Find the prime factorization of 120 using the ladder method. Do NOT write an equation; just write the expression. Provide your answer below:
2×2×2×3×5 2^3×3×5 Divide the number by the smallest prime, which is 2. 602120 Continue dividing by 2 until it no longer divides evenly. 152302602120 Divide by the next prime, 3. 53152302602120 The quotient, 5, is prime so the ladder is complete and we can write the prime factorization of 120 as 2×2×2×3×523×3×5
Find the prime factorization of 1274 using the ladder method.
2×7×7×13 2×7^2×13 Divide the number by the smallest prime, which is 2. 63721274 Divide by the next prime, 7. 91763721274 Continue dividing by 7 until it no longer divides evenly. 13791763721274 The quotient, 13, is prime so the ladder is complete and we can write the prime factorization of 1274 as 2×7×7×13 2×7^2×13
Find the prime factorization of 1274 using the ladder method. Provide your answer below:
2×7×7×13 2×7^2×13 Divide the number by the smallest prime, which is 2. 63721274 Divide by the next prime, 7. 91763721274 Continue dividing by 7 until it no longer divides evenly. 13791763721274 The quotient, 13, is prime so the ladder is complete and we can write the prime factorization of 1274 as anzw above
Find the prime factorization of 1352 using the ladder method. Provide your answer below:
2⋅2⋅2⋅13⋅13 2^3⋅13^2 Divide the number by the smallest prime, which is 2. 67621352 Continue dividing by 2 until it no longer divides evenly.1692338267621352Divide by the next prime, 13.13131692338267621352The quotient, 13, is prime so the ladder is complete and we can write the prime factorization of 1352 as2⋅2⋅2⋅13⋅13 2^3⋅13^2
Find the prime factorization of 232 using the ladder method. Provide your answer below:
2⋅2⋅2⋅29 2^3⋅29 Divide the number by the smallest prime, which is 2. 1162232 Continue dividing by 2 until it no longer divides evenly.2925821162232The quotient, 29, is prime so the ladder is complete and we can write the prime factorization of 232 as2⋅2⋅2⋅2923⋅29
Find the prime factorization of 368 using the ladder method. Note: Please use the multiplication symbol ( × ) in between your numbers, as opposed to the variable x. Provide your answer below:
2⋅2⋅2⋅2⋅23 2^4⋅23 Divide the number by the smallest prime, which is 2. 1842368 Continue dividing by 2 until it no longer divides evenly. 2324629221842368 The quotient, 23, is prime so the ladder is complete and we can write the prime factorization of 368 as 2⋅2⋅2⋅2⋅23 2^4⋅23
Find the prime factorization of 784 using the ladder method. Provide your answer below:
2⋅2⋅2⋅2⋅7⋅7 2^4⋅7^2 Divide the number by the smallest prime, which is 2. 3922784 Continue dividing by 2 until it no longer divides evenly. 49298219623922784 Divide by the next prime, 7. 7749298219623922784 The quotient, 7, is prime so the ladder is complete and we can write the prime factorization of 784 as 2⋅2⋅2⋅2⋅7⋅724⋅72
Find the prime factorization of 296 using the ladder method. use the dot multiplier symbol on the keyboard when entering your answer. Provide your answer below:
2⋅2⋅2⋅37 2^3⋅37 Divide the number by the smallest prime, which is 2. 1482296 Continue dividing by 2 until it no longer divides evenly. 3727421482296 The quotient, 37, is prime so the ladder is complete and we can write the prime factorization of 296 as whats above
Find the prime factorization of 296 using the ladder method. use the dot multiplier symbol on the keyboard when entering your answer. Provide your answer below:
2⋅2⋅2⋅37 2^3⋅37 Divide the number by the smallest prime, which is 2. 1482296 Continue dividing by 2 until it no longer divides evenly.3727421482296The quotient, 37, is prime so the ladder is complete and we can write the prime factorization of 296 as 2⋅2⋅2⋅37 2^3⋅37
Find the prime factorization of 1412 using the ladder method.
2⋅2⋅353 2^2⋅353 Divide the number by the smallest prime, which is 2. 70621412 Continue dividing by 2 until it no longer divides evenly. 353270621412 The quotient, 353, is prime so the ladder is complete and we can write the prime factorization of 1412 as answ above
Find the prime factorization of 1068 using the ladder method. Provide your answer below:
2⋅2⋅3⋅89 2^2⋅3⋅89 Divide the number by the smallest prime, which is 2. 53421068 Continue dividing by 2 until it no longer divides evenly.267253421068Divide by the next prime, 3.893267253421068The quotient, 89, is prime so the ladder is complete and we can write the prime factorization of 1068 as2⋅2⋅3⋅8922⋅3⋅89
Find the prime factorization of 580 using the ladder method. Provide your answer below:
2⋅2⋅5⋅29 2^2⋅5⋅29 Divide the number by the smallest prime, which is 2. 2902580 Continue dividing by 2 until it no longer divides evenly. 14522902580 Divide by the next prime, 5. 29514522902580 The quotient, 29, is prime so the ladder is complete and we can write the prime factorization of 580 as 2⋅2⋅5⋅29 2^2⋅5⋅29
Find the prime factorization of 1194 using the ladder method. Provide your answer below:
2⋅3⋅199 Divide the number by the smallest prime, which is 2. 59721194 Divide by the next prime, 3. 199359721194 The quotient, 199, is prime so the ladder is complete and we can write the prime factorization of 1194 as 2⋅3⋅199
Find the prime factorization of 1173 using a factor tree. Use the multiplication sign, ×, instead of the letter x to separate the factors. It can be found on the keyboard provided below. Provide your answer below:
3⋅17⋅23 A prime factor tree for 1173 is shown below. The figure shows a factor tree for the number 1173.Two branches descend from 1173 and terminate at 3 and 391 respectively. Since 3 is prime it is circled.Two more branches descend from 391 and terminate at 17 and 23 respectively, which are both prime and therefore circled. Note that your factor tree may look different if you started with a different pair of factors, but the circled primes you end up with should be the same.The prime factorization of 1173 is given by the product of the circled primes 3⋅17⋅23
Find the prime factorization of 1281 using the ladder method. Provide your answer below:
3⋅7⋅61 Divide the number by the smallest prime, which is 3. 427 3 1281 Divide by the next prime, 7.61742731281The quotient, 61, is prime so the ladder is complete and we can write the prime factorization of 1281 as3⋅7⋅61
Find the prime factorization of 275 using a factor tree. Use the multiplication sign, ×, instead of the letter x to separate the factors. It can be found on the keyboard provided below.
5^2⋅11 A prime factor tree for 275 is shown below. The figure shows a factor tree for the number 275.Two branches descend from 275 and terminate at 5 and 55 respectively. Since 5 is prime it is circled.Two more branches descend from 55 and terminate at 5 and 11 respectively, which are both prime and therefore circled. Note that your factor tree may look different if you started with a different pair of factors, but the circled primes you end up with should be the same.The prime factorization of 275 is given by the product of the circled primes 5⋅5⋅1152⋅11
Find the prime factorization of 931 using a factor tree. Use the multiplication sign, ×, instead of the letter x to separate the factors. It can be found on the keyboard provided below. Provide your answer below:
7² × 19. A prime factor tree for 931 is shown below. The figure shows a factor tree for the number 931.Two branches descend from 931 and terminate at 7 and 133 respectively. Since 7 is prime it is circled.Two more branches descend from 133 and terminate at 7 and 19 respectively, which are both prime and therefore circled. Note that your factor tree may look different if you started with a different pair of factors, but the circled primes you end up with should be the same.The prime factorization of 931 is given by the product of the circled primes 7×7×1972×19
Prime Numbers and Composite Numbers
A prime number is a counting number greater than 1 whose only factors are 1 and itself. A composite number is a counting number that is not prime.
Identify the number 1075 as either prime or composite. Select the correct answer below: Prime Composite
Composite Test each prime, in order, to see if it is a factor of 1075, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 1075?2Last digit is not 0, 2, 4, 6, or 8.No.31+0+7+5=13 and 13 is not divisible by 3.No.5The last digit of 1075 is 5.Yes. Since 1075 is divisible by 5 we know it is not prime. It is composite.
identify the number 1159 as either prime or composite. Select the correct answer below: Prime Composite
Composite Test each prime, in order, to see if it is a factor of 1159, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 1159?2Last digit is not 0, 2, 4, 6, or 8.No.31+1+5+9=16 and 16 is not divisible by 3.No.5The last digit is not 5 or 0.No.71159÷7=165.571...No.111159÷11=105.364...No.131159÷13=89.154...No.171159÷17=68.176...No.191159÷19=61 Since 1159 is divisible by 19 we know it is not prime. It is composite.
Identify the number 341 as either prime or composite.
Composite Test each prime, in order, to see if it is a factor of 341, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 341?2Last digit is not 0, 2, 4, 6, or 8.No.33+4+1=8 and 8 is not divisible by 3.No.5The last digit is not 5 or 0.No.7341÷7=48.714...No.11341÷11=31Yes. Since 341 is divisible by 11 we know it is not prime. It is composite.
Identify the number 49 as either prime or composite. Select the correct answer below: Prime Composite
Composite Test each prime, in order, to see if it is a factor of 49, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 49?2Last digit is not 0, 2, 4, 6, or 8.No.34+9=13 and 13 is not divisible by 3.No.5The last digit is not 5 or 0.No.749÷7=7Yes. Since 49 is divisible by 7 we know it is not prime. It is composite.
Identify the number 679 as either prime or composite.
Composite Test each prime, in order, to see if it is a factor of 679, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 679? 2 Last digit is not 0, 2, 4, 6, or 8.No. 3 6+7+9=22 and 22 is not divisible by 3.No. 5 The last digit is not 5 or 0.No. 7 679÷7=97 Yes. Since 679 is divisible by 7 we know it is not prime. It is composite.
Identify the number 679 as either prime or composite. Select the correct answer below: Prime Composite
Composite Test each prime, in order, to see if it is a factor of 679, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 679?2Last digit is not 0, 2, 4, 6, or 8.No.36+7+9=22 and 22 is not divisible by 3.No.5The last digit is not 5 or 0.No.7679÷7=97Yes. Since 679 is divisible by 7 we know it is not prime. It is composite.
Identify the number 689 as either prime or composite. Select the correct answer below: Prime Composite FEEDBACK MORE INSTRUCTION
Composite Test each prime, in order, to see if it is a factor of 689, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 689?2Last digit is not 0, 2, 4, 6, or 8.No.36+8+9=23 and 23 is not divisible by 3.No.5The last digit is not 5 or 0.No.7689÷7=98.429...No.11689÷11=62.636...No.13689÷13=53Yes. Since 689 is divisible by 13 we know it is not prime. It is composite.
2⋅2⋅2⋅2⋅2324⋅23 Find the prime factorization of 368 using the ladder method. Note: Please use the multiplication symbol ( × ) in between your numbers, as opposed to the variable x. Provide your answer below:
Divide the number by the smallest prime, which is 2. 1842368 Continue dividing by 2 until it no longer divides evenly.2324629221842368The quotient, 23, is prime so the ladder is complete and we can write the prime factorization of 368 as2⋅2⋅2⋅2⋅2324⋅23
Find the prime factorization of 784 using the ladder method.
Divide the number by the smallest prime, which is 2. 3922784 Continue dividing by 2 until it no longer divides evenly.49298219623922784Divide by the next prime, 7.7749298219623922784The quotient, 7, is prime so the ladder is complete and we can write the prime factorization of 784 as 2⋅2⋅2⋅2⋅7⋅7 2^4⋅7^2
Find the least common multiple of 40 and 8. Provide your answer below:
LCM=40 Method 1: Make lists of the first few multiples of 40 and 8, and use them to find the least common multiple. 408:40,80,120,160,200,240,280:8,16,24,32,40,48,56 Look for the smallest number that appears in both lists.408:40,80,120,160,200,240,280:8,16,24,32,40,48,56The first number to appear on both lists is 40, so the least common multiple of 40 and 8 is 40.Method 2: We can also find the LCM of 40 and 8 using the prime factors methodStep 1. Write each number as a product of primes. The figure shows a factor tree for the number 40.Two branches descend from 40 and terminate at 2 and 20 respectively. Since 2 is prime it is circled.Two more branches descend from 20 and terminate at 2 and 10 respectively. Since 2 is prime it is circled.Two more branches descend from 10 and terminate at 2 and 5 respectively, which are both prime and therefore circled. The figure shows a factor tree for the number 8.Two branches descend from 8 and terminate at 2 and 4 respectively. Since 2 is prime it is circled.Two more branches descend from 4 and terminate at 2 and 2 respectively, which are both prime and therefore circled. Step 2. List the primes of each number, matching primes vertically when possible. 408==22⋅⋅22⋅⋅22⋅5 Step 3. Bring down the number from each column.408LCM===222⋅⋅⋅222⋅⋅⋅222⋅⋅55Step 4. Multiply the factors. LCM=40
Use either the multiples method or the prime factors method to find the least common multiple of 15 and 25.
LCM=75 Method 1: Make lists of the first few multiples of 15 and 25, and use them to find the least common multiple. 1525:15,30,45,60,75,90,105:25,50,75,100,125,150,175 Look for the smallest number that appears in both lists.1525:15,30,45,60,75,90,105:25,50,75,100,125,150,175The first number to appear on both lists is 75, so the least common multiple of 15 and 25 is 75.Method 2: We can also find the LCM of 15 and 25 using the prime factors methodStep 1. Write each number as a product of primes. The figure shows a factor tree for the number 15.Two branches descend from 15 and terminate at 3 and 5 respectively, which are both prime and therefore circled. The figure shows a factor tree for the number 25.Two branches descend from 25 and terminate at 5 and 5 respectively, which are both prime and therefore circled. Step 2. List the primes of each number, matching primes vertically when possible. 1525==3⋅55⋅5 Step 3. Bring down the number from each column.1525LCM===33⋅⋅555⋅⋅55Step 4. Multiply the factors. LCM=75
The table below lists the counting numbers from 2 through 20 along with their factors. The numbers with only two factors are prime, numbers with more than two factors are composite.
Number FactorsPrime or Composite?21,2Prime31,3Prime41,2,4Composite51,5Prime61,2,3,6Composite71,7Prime81,2,4,8Composite91,3,9Composite101,2,5,10Composite111,11Prime121,2,3,4,6,12Composite131,13Prime141,2,7,14Composite151,3,5,15Composite161,2,4,8,16Composite171,17Prime181,2,3,6,9,18Composite191,19Prime201,2,4,5,10,20Composite The prime numbers less than 20 are 2,3,5,7,11,13,17, and 19. There are many larger prime numbers too. To determine whether a number is prime or composite, we need to see if the number has any factors other than 1 and itself. To do this, we can test each of the smaller prime numbers to see if it is a factor of the number. If none of the prime numbers are factors, then that number is also prime.
Identify the number 331 as either prime or composite. Select the correct answer below: Prime Composite
Prime Test each prime, in order, to see if it is a factor of 331, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 331?2Last digit is not 0, 2, 4, 6, or 8.No.33+3+1=7 and 7 is not divisible by 3.No.5The last digit is not 5 or 0.No.7331÷7=47.286...No.11331÷11=30.091...No.13331÷13=25.462...No.17331÷17=19.471...No.19331÷19=17.421...No. We can stop before we get to the next prime, 19, because the quotient will be less than the divisor. We did not find any prime numbers that are factors of 331 so we know 331 is prime.
Identify the number 131 as either prime or composite. Select the correct answer below: Prime Composite
Prime Test each prime, in order, to see if it is a factor of 131, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 131?2Last digit is not 0, 2, 4, 6, or 8.No.31+3+1=5 and 5 is not divisible by 3.No.5The last digit is not 5 or 0.No.7131÷7=18.714...No.11131÷11=11.909...No. We can stop before we get to the next prime, 13, because the quotient will be less than the divisor. We did not find any prime numbers that are factors of 131 so we know 131 is prime.
identify the number 211 as either prime or composite. Select the correct answer below: Prime Composite
Prime Test each prime, in order, to see if it is a factor of 211, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 211?2Last digit is not 0, 2, 4, 6, or 8.No.32+1+1=4 and 4 is not divisible by 3.No.5The last digit is not 5 or 0.No.7211÷7=30.143...No.11211÷11=19.182...No.13211÷13=16.231...No. We can stop before we get to the next prime, 17, because the quotient will be less than the divisor. We did not find any prime numbers that are factors of 211 so we know 211 is prime.
Identify the number 257 as either prime or composite.
Prime Test each prime, in order, to see if it is a factor of 257, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 257?2Last digit is not 0, 2, 4, 6, or 8.No.32+5+7=14 and 14 is not divisible by 3.No.5The last digit is not 5 or 0.No.7257÷7=36.714...No.11257÷11=23.364...No.13257÷13=19.769...No.17257÷17=15.118...No. We can stop before we get to the next prime, 17, because the quotient will be less than the divisor. We did not find any prime numbers that are factors of 257 so we know 257 is prime.
Identify the number 373 as either prime or composite. Select the correct answer below: Prime Composite
Prime Test each prime, in order, to see if it is a factor of 373, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 373?2Last digit is not 0, 2, 4, 6, or 8.No.33+7+3=13 and 13 is not divisible by 3.No.5The last digit is not 5 or 0.No.7373÷7=53.286...No.11373÷11=33.909...No.13373÷13=28.692...No.17373÷17=21.941...No.19373÷19=19.632...No. We can stop before we get to the next prime, 23, because the quotient will be less than the divisor. We did not find any prime numbers that are factors of 373 so we know 373 is prime.
Identify the number 383 as either prime or composite. Select the correct answer below: Prime Composite
Prime Test each prime, in order, to see if it is a factor of 383, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 383?2Last digit is not 0, 2, 4, 6, or 8.No.33+8+3=14 and 14 is not divisible by 3.No.5The last digit is not 5 or 0.No.7383÷7=54.714...No.11383÷11=34.818...No.13383÷13=29.462...No.17383÷17=22.529...No.19383÷19=20.158...No. We can stop before we get to the next prime, 23, because the quotient will be less than the divisor. We did not find any prime numbers that are factors of 383 so we know 383 is prime.
Identify the number 47 as either prime or composite. Select the correct answer below: Prime Composite
Prime Test each prime, in order, to see if it is a factor of 47, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 47?2Last digit is not 0, 2, 4, 6, or 8.No.34+7=11 and 11 is not divisible by 3.No.5The last digit is not 5 or 0.No.747÷7=6.714...No. We can stop before we get to the next prime, 7, because the quotient will be less than the divisor. We did not find any prime numbers that are factors of 47 so we know 47 is prime.
Identify the number 73 as either prime or composite. Select the correct answer below: Prime Composite
Prime Test each prime, in order, to see if it is a factor of 73, starting with 2 as shown.We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 73?2Last digit is not 0, 2, 4, 6, or 8.No.37+3=10 and 10 is not divisible by 3.No.5The last digit is not 5 or 0.No.773÷7=10.429...No. We can stop before we get to the next prime, 11, because the quotient will be less than the divisor. We did not find any prime numbers that are factors of 73 so we know 73 is prime. FEEDBACK
Example Question: Identify each number as prime or composite. ⓐ 83 ⓑ 77
Solution: ⓐ Test each prime, in order, to see if it is a factor of 83, starting with 2, as shown. We will stop when the quotient is smaller than the divisor. PrimeTestFactor of 83?2Last digit of 83 is not 0,2,4,6, or 8.No.38+3=11, and 11 is not divisible by 3.No.5The last digit of 83 is not 5 or 0.No.783÷7=11.857...No.1183÷11=7.545...No. We can stop when we get to 11 because the quotient (7.545...) is less than the divisor. We did not find any prime numbers that are factors of 83, so we know 83 is prime. ⓑ Test each prime, in order, to see if it is a factor of 77. PrimeTestFactor of 77?2Last digit is not 0,2,4,6, or 8.No.37+7=14, and 14 is not divisible by 3.No.5the last digit is not 5 or 0.No.777÷11=7Yes. Since 77 is divisible by 7, we know it is not a prime number. It is composite.
Identify Prime and Composite Numbers
Some numbers, like 72, have many factors. Other numbers, such as 7, have only two factors: 1 and the number. A number with only two factors is called a prime number. A number with more than two factors is called a composite number. The number 1 is neither prime nor composite. It has only one factor: itself.
How To Find the Prime Factorization of a Composite Number Using the Ladder Method
Step 1. Divide the number by the smallest prime. Step 2. Continue dividing by that prime until it no longer divides evenly. Step 3. Divide by the next prime until it no longer divides evenly. Step 4. Continue until the quotient is a prime. Step 5. Write the composite number as the product of all the primes on the sides and top of the ladder.
How To Determine if a number is prime.
Step 1. Test each of the primes, in order, to see if it is a factor of the number. Step 2. Start with 2 and stop when the quotient is smaller than the divisor or when a prime factor is found. Step 3. If the number has a prime factor, then it is a composite number. If it has no prime factors, then the number is prime.
Find the Prime Factorization Using the Ladder Method
The ladder method is another way to find the prime factors of a composite number. It leads to the same result as the factor tree method. Some people prefer the ladder method to the factor tree method, and vice versa. To begin building the "ladder," divide the given number by its smallest prime factor. For example, to start the ladder for 36, we divide 36 by 2, the smallest prime factor of 36. 18236 To add a "step" to the ladder, we continue dividing by the same prime until it no longer divides evenly. 9218236 Then we divide by the next prime; so, we divide 9 by 3. 339218236 We continue dividing up the ladder in this way until the quotient is prime. Since the quotient, 3, is prime, we stop here. Do you see why the ladder method is sometimes called stacked division? The prime factorization is the product of all the primes on the sides and top of the ladder. 2⋅2⋅3⋅3 2^2⋅3^2 Notice that the result is the same as we obtained with the factor tree method.
