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**Factors, Primes & Composite Numbers**

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**Definition Product Product – An answer to a multiplication problem.**

7 x 8 = 56 Product

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Definition Factor – a number that is multiplied by another to give a product. 7 x 8 = 56 Factors

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Definition Factor – a number that divides evenly into another. 56 ÷ 8 = 7 Factor

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What are the factors? 6 x 7 = 42 6 & 7 7 x 9 = 63 7 & 9 8 x 6 = 48 8 & 6 4 & 9 4 x 9 = 36

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What are the factors? 42 ÷ 7 = 6 7 63 ÷ 9 = 7 9 48 ÷ 6 = 8 6 9 36 ÷ 9 = 4

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**7 Definition 7 is prime because the only numbers**

Prime Number – a number that has only two factors, itself and 1. 7 7 is prime because the only numbers that will divide into it evenly are 1 and 7.

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**Examples of Prime Numbers**

2, 3, 5, 7, 11, 13, 17, 19 Special Note: One is not a prime number.

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**8 Definition The factors of 8 are 1, 2, 4, 8**

Composite number – a number that has more than two factors. 8 The factors of 8 are 1, 2, 4, 8

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**Examples of Composite Numbers**

4, 6, 8, 9, 10, 12, 14, 15 Special Note: Every whole number from 2 on is either composite or prime.

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**Our Lonely 1 One is not a prime nor a composite number.**

It is not prime because it does not have exactly two different factors. It is not composite because it does not have more than 2 factors. Special Note: One is not a prime nor a composite number.

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Definition Prime Factorization – A way to write a composite number as the product of prime factors. 2 x 2 x 3 = 12 or 2 2 x 3 = 12

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**How to Do Prime Factorization Using a Factor Tree**

Step 1 – Start with a composite number. 48 Step 2 – Write down a multiplication problem that equals this number or any pair of factors of this number. 6 x 8 = 48

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**How to Do Prime Factorization Using a Factor Tree**

Step 3 – Find factors of these factors. 6 x 8 = 48 2 x 3 x 2 x 4 = 48

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**How to Do Prime Factorization Using a Factor Tree**

Step 4 – Find factors of these numbers until all factors are prime numbers. 6 x 8 = 48 2 x 3 x 2 x 4 = 48 2 x 3 x 2 x 2 x 2 = 48

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**How to Do Prime Factorization Using a Factor Tree**

Step 5 – Write the numbers from least to greatest. 6 x 8 = 48 2 x 3 x 2 x 2 x 2 = 48 2 x 2 x 2 x 2 x 3 = 48

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**How to Do Prime Factorization Using a Factor Tree**

Step 6 – Count how many numbers are the same and write exponents for them. 6 x 8 = 48 2 x 3 x 2 x 2 x 2 = 48 2 x 2 x 2 x 2 x 3 = 48 4 2 x 3 = 48

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**Prime factor this number**

4 2 x 2 = 4 2 2 = 4

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**Prime factor this number**

6 2 x 3 = 6

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**Prime factor this number**

8 2 x 4 = 8 2 x 2 x 2 = 8 3 2 = 8

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**Prime factor this number**

9 3 x 3 = 9 2 3 = 9

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**Prime factor this number**

10 2 x 5 = 10

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**Prime factor this number**

12 3 x 4 = 12 3 x 2 x 2 = 12 2 x 2 x 3 = 12 2 2 x 3 = 12

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**Prime factor this number**

14 2 x 7 = 14

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**Prime factor this number**

15 3 x 5 = 15

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**Prime factor this number**

16 4 x 4 = 16 2 x 2 x 2 x 2 = 16 4 2 = 16

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**Prime factor this number**

18 3 x 6 = 18 3 x 2 x 3 = 18 2 x 3 x 3 = 18 2 x 3 = 18 2

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**Prime factor this number**

20 4 x 5 = 20 2 x 2 x 5 = 20 2 x 5 = 20 2

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**Prime factor this number**

21 3 x 7 = 21

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**Prime factor this number**

22 2 x 11 = 22

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**What about those with variables?**

24y2 We do the same as before, we just add the variables with it 2 * 2 * 2 * 3 * y * y 23 * 3 * y2

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**4-5 Greatest Common Factor**

Example Use prime factorization to find the GCF of 42 and 70.

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**4-5 Greatest Common Factor**

Example Use prime factorization to find the GCF of 42 and 70. First find the prime factorization of each number. 42 = 7 * = 7 * 10

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**4-5 Greatest Common Factor**

Example Use prime factorization to find the GCF of 42 and 70. First find the prime factorization of each number. 42 = 7 * = 7 * 10 = 7 * 2 * = 7 * 2 * 5

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**4-5 Greatest Common Factor**

Example Use prime factorization to find the GCF of 42 and 70. First find the prime factorization of each number. 42 = 7 * = 7 * 10 = 7 * 2 * = 7 * 2 * 5 Then find the common factors. 42 = 7 * 2 * 3 70 = 7 * 2 * 5

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**4-5 Greatest Common Factor**

Example Use prime factorization to find the GCF of 42 and 70. First find the prime factorization of each number. 42 = 7 * = 7 * 10 = 7 * 2 * = 7 * 2 * 5 Then find the common factors. 42 = 7 * 2 * 3 70 = 7 * 2 * 5

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**4-5 Greatest Common Factor**

Example Use prime factorization to find the GCF of 42 and 70. First find the prime factorization of each number. 42 = 7 * = 7 * 10 = 7 * 2 * = 7 * 2 * 5 Then find the common factors. 42 = 7 * 2 * 3 70 = 7 * 2 * 5 The greatest common factor of 42 and 70 is 2 * 7 or 14.

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**4-5 Greatest Common Factor**

Example Find the greatest common factor of 6m2 and 15m

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**4-5 Greatest Common Factor**

Example Find the greatest common factor of 6m2 and 15m First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m

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**4-5 Greatest Common Factor**

Example Find the greatest common factor of 6m2 and 15m First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m = 3 * 2 * m * m = 3 * 5 * m

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**4-5 Greatest Common Factor**

Example Find the greatest common factor of 6m2 and 15m First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m = 3 * 2 * m * m = 3 * 5 * m Then find the common factors. 6m2 = 3 * 2 * m * m 15m = 3 * 5 * m

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**4-5 Greatest Common Factor**

Example Find the greatest common factor of 6m2 and 15m First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m = 3 * 2 * m * m = 3 * 5 * m Then find the common factors. 6m2 = 3 * 2 * m * m 15m = 3 * 5 * m

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**4-5 Greatest Common Factor**

Example Find the greatest common factor of 6m2 and 15m First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m = 3 * 2 * m * m = 3 * 5 * m Then find the common factors. 6m2 = 3 * 2 * m * m 15m = 3 * 5 * m The greatest common factor of 6m2 and 15m is 3 * m or 3m.

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