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4.2 Factors and Prime Factorization Learn to write prime factorizations of composite numbers. Vocabulary factor prime factorization Prime Number Brain Pop 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 Factors 6÷2=3 Product 6 is divisible by 3 and 2. Helpful Hint When the pairs of factors begin to repeat, then you have found all of the factors of the number you are factoring. Additional Example 1A: Finding Factors List all of the factors of the number 16. A. 16 16 = 1 • 16 16 = 2 • 8 16 = 4 • 4 16 = 8 • 2 1 2 4 4 1 2 3 4 5 6 7 8 is a factor. is a factor. is not a factor. is a factor. is not a factor. is not a factor. is not a factor. and 2 have already been listed so stop here. 8 16 You can draw a diagram to illustrate the factor pairs. The factors of 16 are 1, 2, 4, 8, and 16. 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. You can use factors to write a number in different ways. Factorization of 12 1 • 12 2•6 3•4 3•2•2 Notice that these factors are all prime. Prime factorization A way to write a composite number as the product of prime factors. 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 2 • 24 2 • 6 12 • 6 2 • 3 3 • 2 4 2 • 2 24 = 3 • 2 • 2 • 2 24 = 2 • 2 • 2 • 3 The prime factorization of 24 is 2 • 2 • 2 • 3, or 23 • 3. 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 2 • 28 14 2 • 7 7 28 = 2 • 2 • 7 • 4 2 • 2 28 = 7 • 2 • 2 The prime factorization of 28 is 2 • 2 • 7, or 22 • 7 . Prime factor this number 12 3 x 4 = 12 3 x 2 x 2 = 12 2 x2 2 x 3 = 12 2 x 3 = 12 Prime factor this number 14 2 x 7 = 14 Prime factor this number 18 3 x 6 = 18 3 x 2 x 3 = 18 2 x 3 x 3 = 18 2 2 x 3 = 18 Watch……. Factoring Brain Pop