Section 2.4 Part 1: Identify Multiples and Use Divisibility Tests *need to practice this*
Determine whether 425 is a multiple of 10.
No, 425 is not a multiple of 10. To solve, ask yourself if the last digit of 425 is zero. It isn't; therefore, 425 is not a multiple of 10.
Which of the following numbers is a multiple of 3?
So, the numbers 174 and 501 are divisible by 3. Is 174 a multiple of?Test Multiple?3 1+7+4=12 and 12 is divisible by 3.Yes. Is 314 a multiple of?Test Multiple?3 3+1+4=8 and 8 is not divisible by 3.No. Is 501 a multiple of?Test Multiple?3 5+0+1=6 and 6 is divisible by 3.Yes. Is 541 a multiple of?Test Multiple?3 5+4+1=10 and 10 is not divisible by 3.No. Is 1232 a multiple of?Test Multiple?3 1+2+3+2=8 and 8 is not divisible by 3.No.So, the numbers 174 and 501 are divisible by3.
Question: Determine whether 350 is a multiple of 10.
Solution: To solve, ask yourself if the last digit of 350 is zero. It is; therefore, 350 is a multiple of 10.
Use the divisibility tests to determine which of the given numbers 729000 is divisible by. Select all that apply: 2 3 5 6 10
2 3 5 6 10 Use the divisibility tests to check if 729000 is divisible by each of the given numbers. Divisible by...?TestDivisible?2The last digit of 729000 is 0.Yes.37+2+9+0+0+0=18 and 18 is divisible by 3.Yes.5The last digit of 729000 is 0.Yes.6729000 is divisible by both 2 and 3Yes.10The last digit of 729000 is 0.Yes. So, 729000 is divisible by the numbers 2, 3, 5, 6, and 10.
Use the divisibility tests to determine which of the given numbers 50 is divisible by. Select all that apply. Select all that apply: 2 3 5 6 10
2 5 10 Use the divisibility tests to check if 50 is divisible by each of the given numbers. Divisible by...?TestDivisible? 2 The last digit of 50 is 0.Yes. 3 5+0=5 and 5 is not divisible by 3.No. 5 The last digit of 50 is 0.Yes. 6 50 is not divisible by both 2 and 3No. 10 The last digit of 50 is 0.Yes. So, 50 is divisible by the numbers 2, 5, and 10.
Question: Determine whether579 is a multiple of 5.
Solution: To solve, ask yourself if the last digit of 579 is a 5 or a 0. It isn't; therefore, 579 is not a multiple of 5.
Use the divisibility tests to determine which of the given numbers 2172 is divisible by. Select all that apply: 2 3 5 6 10
Select all that apply: 2 3 6 Use the divisibility tests to check if 2172 is divisible by each of the given numbers. Divisible by...?TestDivisible?2The last digit of 2172 is 2.Yes.32+1+7+2=12 and 12 is divisible by 3.Yes.5The last digit is not 5 or 0.No.62172 is divisible by both 2 and 3Yes.10The last digit of 2172 is not 0.No. So,2172is divisible by the numbers2,3, and6.
Question Use the divisibility tests to determine which of the given numbers 3470 is divisible by. Select all that apply: 2 3 5 6 10
So, 3470 is divisible by the numbers 2, 5, and 10. Use the divisibility tests to check if 3470 is divisible by each of the given numbers. Divisible by...?TestDivisible? 2 The last digit of 3470 is 0.Yes. 3 3+4+7+0=14 and 14 is not divisible by 3.No. 5 The last digit of 3470 is 0.Yes .6 3470 is not divisible by both 2 and 3No. 10 The last digit of 3470 is 0.Yes. So, 3470 is divisible by the numbers 2, 5, and 10.
Question: Determine whether 645 is a multiple of 3.
Solution: To solve, find the sum of the digits. 6+4+5=15 Is 15 a multiple of 3? Yes, so 645 is a multiple of 3 too. If we're not sure, we could add its digits to find out. We can check it by dividing 645 by 3. 645÷3 The quotient is 215. 3⋅215=645
Question: Determine whether each of the following is a multiple of 2: ⓐ489 ⓑ 3,714
Solution: ⓐ Is 489 a multiple of 2? To solve, ask yourself if the last digit is 0, 2, 4, 6, or 8. It isn't; therefore, 489 is not a multiple of 2. ⓑ Is 3,714 a multiple of 2? To solve, ask yourself if the last digit of 3,714 is 0, 2, 4, 6, or 8. It is; therefore, 3,714 is a multiple of 2.
Now let's look at multiples of 5. The table below highlights all of the multiples of 5 between 1 and 50. What do you notice about the multiples of 5?
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950 All multiples of 5 end with either 5 or 0. Just like we identify multiples of 2 by looking at the last digit, we can identify multiples of 5 by looking at the last digit.
Identify Multiples of Numbers Annie is counting the shoes in her closet. The shoes are matched in pairs, so she doesn't have to count each one. She counts by twos: 2, 4, 6, 8, 10, 12. She has 12 shoes in her closet. The numbers 2, 4, 6, 8, 10, and 12 are called multiples of 2. Multiples of 2 can be written as the product of a counting number and 2. The first six multiples of 2 are given below.
1⋅2=2 2⋅2=4 3⋅2=6 4⋅2=8 5⋅2=10 6⋅2=12
A multiple of a number is the product of the number and a counting number. So, a multiple of 3 would be the product of a counting number and 3. Below are the first six multiples of 3.
1⋅3=3 2⋅3=6 3⋅3=9 4⋅3=12 5⋅3=15 6⋅3=18
Use the divisibility tests to determine which of the given numbers 290250 is divisible by. Select all that apply: 2 3 5 6 10
2 3 5 6 10 Use the divisibility tests to check if 290250 is divisible by each of the given numbers. Divisible by...?TestDivisible? 2 The last digit of 290250 is 0.Yes. 3 2+9+0+2+5+0=18 and 18 is divisible by 3.Yes. 5 The last digit of 290250 is 0.Yes .6 290250 is divisible by both 2 and 3Yes .10 The last digit of 290250 is 0.Yes. So, 290250 is divisible by the numbers 2, 3, 5, 6, and 10.
Use the divisibility tests to determine which of the given numbers 838 is divisible by. Select the correct answer below: 2 3 5 6 10
2 Use the divisibility tests to check if 838 is divisible by each of the given numbers. Divisible by...?TestDivisible? 2 The last digit of 838 is 8.Yes. 3 8+3+8=19 and 19 is not divisible by 3.No. 5 The last digit is not 5 or 0.No .6 838 is not divisible by both 2 and 3No .10 The last digit of 838 is not 0.No. So, 838 is divisible by the number 2. FEEDBACK
Use the divisibility tests to determine which of the given numbers 1350 is divisible by.Select all that apply:
2,3,5,6,10
Use the divisibility tests to determine which of the given numbers 8550 is divisible by.
2,3,5,6,10
Use the divisibility tests to determine which of the given numbers 315 is divisible by. Select all that apply: 2 3 5 6 10
3 5 Use the divisibility tests to check if 315 is divisible by each of the given numbers. Divisible by...?TestDivisible? 2 Last digit is not 0, 2, 4, 6, or 8.No .3 3+1+5=9 and 9 is divisible by 3.Yes .5 The last digit of 315 is 5.Yes .6 315 is not divisible by both 2 and 3No. 10 The last digit of 315 is not 0.No. So, 315 is divisible by the numbers 3 and 5.
Use the divisibility tests to determine which of the given numbers 333 is divisible by. Select the correct answer below: 2 3 5 6 10
3 Use the divisibility tests to check if 333 is divisible by each of the given numbers. Divisible by...?TestDivisible? 2 Last digit is not 0, 2, 4, 6, or 8.No. 3 3+3+3=9 and 9 is divisible by 3.Yes. 5 The last digit is not 5 or 0.No. 6 333 is not divisible by both 2 and 3No. 10 The last digit of 333 is not 0.No. So, 333 is divisible by the number 3.
List the first 5 multiples of 3.(Use commas to separate each multiple.)
3,6,9,12,15,
Multiple of a Number
A number is a multiple of n if it is the product of a counting number and n. 1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950 The last digit of each highlighted number in the table above is either 0, 2, 4, 6, or 8. This is true for the product of 2 and any counting number. So, to tell if any number is a multiple of 2 look at the last digit. If it is 0, 2, 4, 6, or 8, then the number is a multiple of 2.
The table below highlights the multiples of 10 between 1 and 50. All multiples of 10 end with a zero. 1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950
All multiples of 10 end with 0. Just like we identify multiples of 2 and multiples of 5 by looking at the last digit, we can identify multiples of 10 by looking for a zero in the last digit.
Determine whether 10,519 is a multiple of 3.
No, 10,519 is not a multiple of 3. No, 10,519 is not a multiple of 3. To solve, find the sum of the digits. 1+0+5+1+9=16 Is 16 a multiple of 3? No, so 10,519 is not a multiple of 3 either. We can check this by dividing 10,519 by 3. 3/10,519= 506R13 When we divide 10,519 by 3, we do not get a counting number, so 10,519 is not the product of a counting number and 3. It is not a multiple of 3.
We can find the multiples of any number by continuing this process. The table below shows the multiples of 2 through 9 for the first 12 counting numbers.
Counting Number 1 2 3 4 5 6 7 8 9 10 11 12 Multiples of 2 2 4 6 8 10 12 14 16 18 20 22 24 Multiples of 3 3 6 9 12 15 18 21 24 27 30 33 36 Multiples of 4 4 8 12 16 20 24 28 32 36 40 44 48 Multiples of 5 5 10 15 20 25 30 35 40 45 50 55 60 Multiples of 6 6 12 18 24 30 36 42 48 54 60 66 72 Multiples of 7 7 14 21 28 35 42 49 56 63 70 77 84 Multiples of 8 8 16 24 32 40 48 56 64 72 80 88 96 Multiples of 9 9 18 27 36 45 54 63 72 81 90 99 108
Which of the following numbers is a multiple of 6? Select the correct answer below:
To figure out which of the given numbers are divisible by 6 we need to apply the divisibility test for 6 to each number. Recall that a number is divisible by 6 if it is divisible by both 2 and 3. Is 127 a multiple of?Test Multiple? 2 Last digit is not 0, 2, 4, 6, or 8 .No. 3 1+2+7=10 and 10 is not divisible by 3.No .6 127 is not divisible by both 2 and 3 No. Is 146 a multiple of?TestMultiple? 2The last digit of 146 is 6.Yes.3 1+4+6=11 and 11 is not divisible by 3.No.6146 is not divisible by both 2 and 3No. Is 318 a multiple of?TestMultiple?2The last digit of 318 is 8.Yes.3 3+1+8=12 and 12 is divisible by 3.Yes.6318 is divisible by both 2 and 3Yes. Is 821 a multiple of?TestMultiple?2Last digit is not 0, 2, 4, 6, or 8.No.3 8+2+1=11 and 11 is not divisible by 3.No.6821 is not divisible by both 2 and 3No. Is 851 a multiple of?TestMultiple?2Last digit is not 0, 2, 4, 6, or 8.No.38+5+1=14 and 14 is not divisible by 3.No.6851 is not divisible by both 2 and 3No. So, the number 318 is divisible by 6.
The table below highlights multiples of 3. The pattern for multiples of 3 is not as obvious as the patterns for multiples of 2, 5, and 10. 1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950 Multiples of 3 between 1 and 50
Unlike the other patterns we've examined so far, this pattern does not involve the last digit. The pattern for multiples of 3 is based on the sum of the digits. If the sum of the digits of a number is a multiple of 3, then the number itself is a multiple of 3. See the table below. Multiple of 33691215182124Sum of digits3691+2=31+5=61+8=92+1=32+4=6 Consider the number 42. The digits are 4 and 2, and their sum is 4+2=6. Since 6 is a multiple of 3, we know that 42 is also a multiple of 3.
Use the divisibility tests to determine which of the given numbers 4950 is divisible by. Select all that apply. Select all that apply: 2 3 5 6 10
Use the divisibility tests to check if 4950 is divisible by each of the given numbers. Divisible by...?TestDivisible? 2 The last digit of 4950 is 0.Yes .3 4+9+5+0=18 and 18 is divisible by 3.Yes. 5 The last digit of 4950 is 0.Yes .6 4950 is divisible by both 2 and 3Yes.10The last digit of 4950 is 0.Yes. So,4950is divisible by the numbers2,3,5,6, and10.
Determine whether 880 is a multiple of 5.
Yes, 880 is a multiple of 5. Is 880 a multiple of 5? Is the last digit of 880 a 5 or 0? Yes. Therefore, 880 is a multiple of 5.
