PRIME AND COMPOSITE NUMBERS Vocabulary Prime Composite One

PRIME AND COMPOSITE NUMBERS

Vocabulary Prime Composite One Factors Products Prime Factorization Factor Trees

Prime numbers have only two factors: only by 1 and the number itself. - Prime numbers are like building blocks of all numbers, and other numbers are 'built' from them. - ALL numbers can be factored down so the factors are just prime numbers. -Prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19.

Example: 13 is a prime number because the only factors of 13 are 1 and 13. The number 8 is not prime because it has four factors: 1, 2, 4 and 8.

Composite Number: is a whole number that has more than two factors. Examples of Composite Numbers 4 = 2 x 2, 4 x 1 10 = 2 x 5, 1 x 10 64 = 1 x 64, 16 x 4, 8 x 8 12 = 1 x 12, 2 x 6, 3 x 4

Factors & Products Remember, what factors are? Factors are numbers you multiply together to get another whole number (no decimals) 4 x 3 = 12 Product Factors Product is the answer to a multplication question

"Prime Factorization" is finding which prime numbers you need to multiply together to get the original number. Prime Factorization can be done using Factor Trees

Factor Trees To find the factors of a larger number, one can use a Factor Tree 180 10 1. Choose two factors of 180 18 2. So we chose 10 and 18.

Factor Trees 180 3. Next, find factors for 10 & 18 18 10 6 x 3 = 18 2 x 5 = 10 2 5 6 3

Factor Trees 180 4. Since 2 and 3 and 5 are PRIME NUMBERS they do not grow “new branches”. They just grow down alone. 18 10 2 2 5 6 3 2 3 3 5 Since 6 is NOT a prime number - it is a COMPOSITE NUMBER - it still has factors. Since it is an EVEN NUMBER we see that: 6 = 2 x 3 x �

Factor Trees Now to check your work. All the prime factors found should multiply together to get the original product Check: 2 x 3 x 5 = 180

Factor Trees Find the prime factors of 36 using factor trees and prime factorization. METHOD 1 36 / 4 9 / / 2 23 3 METHOD 2 36 / 6 6 / / 2 32 3 Sometimes there is more than one way to find the prime factors.

Factor Trees Find the prime factors of 36 using factor trees and prime factorization. METHOD 1 36 / 4 9 / / 2 23 3 2 x 2 x 3 x 3 = 36 The Prime Factors For 36 should be the same no matter which method you use METHOD 2 36 / 6 6 / / 2 32 3 2 x 3 x 2 x 3 = 36

Factor Trees Find the prime factors of 48 using factor trees and prime factorization. 48 / 4 12 / / 2 23 4 | | | / 2 23 22 Check: 2 x 2 x 3 = 48

Find the prime factors of each using factor trees and prime factorization. a) b) c) d) e) f) 144 200 88 54 72 1000

a) 144 a) 200 144 / 12 12 / / 34 3 4 | / 322322 200 / 10 20 / / 2 5 2 10 | | | / 2 5 2 x 2 x 3 x 3 = 144 2 x 2 x 2 x 5 x 5 = 200

e) 72 f) 1000 72 / 8 9 / / 2 4 3 3 | / | | 22233 1000 / 10 100 / / 2 5 10 10 | | / / 2 52 52 5 2 x 2 x 2 x 3 x 3 = 72 2 x 2 x 2 x 5 x 5 x 5= 1000