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Learn to write prime factorizations of composite numbers. 4.2 Factors and Prime Factorization

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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 = Factors Product 2 63 ÷ = 6÷2 = 3 6 is divisible by 3 and 2.

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

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

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Additional Example 1B: Finding Factors List all of the factors of the number 19. B = 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 Prime factorization A way to write a composite number as the product of prime factors. Notice that these factors are all prime.

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Additional Example 2A: Writing Prime Factorizations 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 = = The prime factorization of 24 is , or Write the prime factorization of 24.

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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 = = The prime factorization of 28 is 2 2 7, or

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Prime factor this number 12 3 x 4 2 x 3 = 12 2 = 12 3 x 2 x 2 = 12 2 x 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 2 x 3 = 18 2 = 18 3 x 2 x 3 = 18 2 x 3 x 3 = 18

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Watch……. Factoring Brain Pop

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