prime numbers & composite numbers

A Prime Numbers: are numbers that are only divisible by itself and 1 without a remainder (& must be a whole number greater than 1) .

A Prime Number can be divided evenly only by 1 or itself. And it must be a whole number greater than 1. Example: 7 can only be divided evenly by 1 or 7, so it is a prime number. But 6 can be divided evenly by 1, 2, 3 and 6 so it is NOT a prime number (it is a composite number). Let me explain ... Some whole numbers can be divided up evenly, and some can't! Example: 6 can be divided evenly by 2, or by 3: 6 = 2 × 3 Like this: 6 divided into 2 or 6 divided into 3 divided into 2 groups divided into 3 groups But 7 cannot be divided up evenly: 7 is Prime And we give them names: When a number can be divided up evenly it is a Composite Number When a number can not be divided up evenly it is a Prime Number So 6 is Composite, but 7 is Prime. And that explains it ... but there are some more details ... Not Into Fractions We are only dealing with whole numbers here! We are not going to cut things into halves or quarters. Not Into Groups of 1 OK, we could have divided 7 into seven 1s (or one 7) like this: prime 1x7 7 = 1 x 7 But we could do that for any whole number! So we should also say we are not interested in dividing by 1, or by the number itself. It is a Prime Number when it can't be divided evenly by any number (except 1 or itself). Example: is 7 a Prime Number or Composite Number? 7 is Prime We cannot divide 7 evenly by 2 (we get 2 lots of 3, with one left over) We cannot divide 7 evenly by 3 (we get 3 lots of 2, with one left over) We cannot divide 7 evenly by 4, or 5, or 6. We can only divide 7 into one group of 7 (or seven groups of 1): prime 1x7 7 = 1 x 7 So 7 can only be divided evenly by 1 or itself: So 7 is a Prime Number

Prime Numbers - Facts, Examples, & Table Of All Up To 1,000

A prime number can be divided, without a remainder, only by itself and by 1. For example, 17 can be divided only by 17 and by 1. Some facts: The only even prime number is 2. All other even numbers can be divided by 2. If the sum of a number's digits is a multiple of 3, that number can be divided by 3. No prime number greater than 5 ends in a 5. Any number greater than 5 that ends in a 5 can be divided by 5. Zero and 1 are not considered prime numbers. Except for 0 and 1, a number is either a prime number or a composite number. A composite number is defined as any number, greater than 1, that is not prime. To prove whether a number is a prime number, first try dividing it by 2, and see if you get a whole number. If you do, it can't be a prime number. If you don't get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (9 is divisible by 3) and so on, always dividing by a prime number (see table below). Here is a table of all prime numbers up to 1,000: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997

Factors

Factors We can also define a Prime Number using factors. factor 2x3=6 "Factors" are numbers we multiply together to get another number. And we have: When the only two factors of a number are 1 and the number, then it is a Prime Number It means the same as our previous definition, just stated using factors. And remember this is only about Whole Numbers (1, 2, 3, ... etc), not fractions or negative numbers. So don't say "I could multiply ½ times 6 to get 3" OK? Examples: 3 = 1 × 3 (the only factors are 1 and 3) Prime 6 = 1 × 6 or 6 = 2 × 3 (the factors are 1,2,3 and 6) Composite Examples From 1 to 14 Factors other than 1 or the number itself are highlighted: Number Can be Evenly Divided By Prime, or Composite? 1 (1 is not considered prime or composite) 2 1, 2 Prime 3 1, 3 Prime 4 1, 2, 4 Composite 5 1, 5 Prime 6 1, 2, 3, 6 Composite 7 1, 7 Prime 8 1, 2, 4, 8 Composite 9 1, 3, 9 Composite 10 1, 2, 5, 10 Composite 11 1, 11 Prime 12 1, 2, 3, 4, 6, 12 Composite 13 1, 13 Prime 14 1, 2, 7, 14 Composite ... ... ... So when there are more factors than 1 or the number itself, the number is Composite. A question for you: is 15 Prime or Composite? Why All the Fuss about Prime and Composite? Because we can "break apart" Composite Numbers into Prime Number factors. blocks 2 2 3 It is like the Prime Numbers are the basic building blocks of all numbers. And the Composite Numbers are made up of Prime Numbers multiplied together. Here we see it in action: prime composite 2 is Prime, 3 is Prime, 4 is Composite (=2×2), 5 is Prime, and so on... Example: 12 is made by multiplying the prime numbers 2, 2 and 3 together. 12 = 2 × 2 × 3 The number 2 was repeated, which is OK. In fact we can write it like this using the exponent of 2: 12 = 22 × 3 And that is why they are called "Composite" Numbers because composite means "something made by combining things"

Composite number

It is a Composite Number when it can be divided evenly by numbers other than 1 or itself. Like this: Example: is 6 a Prime Number or Composite Number? 6 can be divided evenly by 2, or by 3, as well as by 1 or 6: 6 = 1 × 6 6 = 2 × 3 So 6 is a Composite Number Sometimes a number can be divided evenly many ways: Example: 12 can be divided evenly by 1, 2, 3, 4, 6 and 12: 1 × 12 = 12 2 × 6 = 12 3 × 4 = 12 So 12 is a Composite Number And note this: Any whole number greater than 1 is either Prime or Composite What About 1? Years ago 1 was included as a Prime, but now it is not: 1 is not Prime and also not Composite. You can also try this Prime Numbers Activity.

HelpHelp Which one of the following numbers is prime? A 18 B 19 C 20 D 21

answer: B. 19 18 is composite because 18 can be written as a product of factors, not including 1 and 18: 18 = 2 × 9 or 18 = 3 × 6 19 is prime because 19 doesn't have any factors except 1 and 19 20 is composite because 20 can be written as a product of factors, not including 1 and 20: 20 = 2 × 10 or 20 = 4 × 5 21 is composite because 21 can be written as a product of factors, not including 1 and 21: 21 = 3 × 7

Which one of the following numbers is composite? A 67 B 69 C 71 D 73

answer: B. 69 67, 71 and 73 are all prime numbers, so cannot be composite. 69 = 3 × 23 is composite.

Which one of the following numbers is prime? A. 26 B. 27 C. 28 D 29

answer: D. 29 26 is composite because 26 can be written as a product of factors, not including 1 and 26: 26 = 2 × 13 27 is composite because 27 can be written as a product of factors, not including 1 and 27: 27 = 3 × 3 × 3 or 33 28 is composite because 28 can be written as a product of factors, not including 1 and 28: 28 = 4 × 7 or 22 × 7 29 is prime because 29 doesn't have any factors except 1 and 29

Prime

it is a prime number when the number cannot be divided evenly by any number except number 1 and itself. example: 7 cannot be divided evenly by other number except by 1 and itself-7. 2 3 5 etc