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**4.2 Factors and Prime Factorization**

Learn to write prime factorizations of composite numbers.

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Vocabulary factor prime factorization Prime Number Brain Pop

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Whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors. 2 3 = 6 6 ÷ 3 = 2 6 is divisible by 3 and 2. 6 ÷ 2 = 3 Factors Product

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Helpful Hint When the pairs of factors begin to repeat, then you have found all of the factors of the number you are factoring.

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**Additional Example 1A: Finding Factors**

List all of the factors of the number 16. A. 16 16 = 1 • 16 1 is a factor. 16 = 2 • 8 2 is a factor. 3 is not a factor. 16 = 4 • 4 4 is a factor. 5 is not a factor. 6 is not a factor. 7 is not a factor. 16 = 8 • 2 8 and 2 have already been listed so stop here. 1 2 4 4 8 16 You can draw a diagram to illustrate the factor pairs. The factors of 16 are 1, 2, 4, 8, and 16.

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**Additional Example 1B: Finding Factors**

List all of the factors of the number 19. B. 19 19 = 1 • 19 19 is not divisible by any other whole number. The factors of 19 are 1 and 19.

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**You can use factors to write a number in different ways.**

Factorization of 12 Notice that these factors are all prime. 1 • 12 2 • 6 3 • 4 3 • 2 • 2 Prime factorization A way to write a composite number as the product of prime factors.

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**Additional Example 2A: Writing Prime Factorizations**

Write the prime factorization of 24. Method 1: Use a factor tree. Choose any two factors of 24 to begin. Keep finding factors until each branch ends at a prime factor. 24 24 • 6 • 2 12 4 2 • 6 3 • 2 2 • 2 2 • 3 24 = 3 • 2 • 2 • 2 24 = 2 • 2 • 2 • 3 The prime factorization of 24 is 2 • 2 • 2 • 3, or 23 • 3.

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**Write the prime factorization of 28.**

Check It Out: Example 2A Write the prime factorization of 28. Method 1: Use a factor tree. Choose any two factors of 28 to begin. Keep finding factors until each branch ends at a prime factor. 28 28 2 • 14 7 • 4 2 • 7 2 • 2 28 = 2 • 2 • 7 28 = 7 • 2 • 2 The prime factorization of 28 is 2 • 2 • 7, or 22 • 7 .

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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**

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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Watch……. Factoring Brain Pop

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Prime Factorization (Factor Trees)

Prime Factorization (Factor Trees)

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