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1.1 Prime Factorization - Greatest Common Factor. Math 8 Sort the following numbers in the table: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Exactly one factor Exactly two factors 2, 3, 5, 7 More than two factors 4, 6, 8, 9, 10 prime composite 1 Neither prime nor composite A whole number with exactly two factors (1 and itself) is called a _ prime __. A whole number greater than 1 with more than two factors is called a __ composite _. The numbers 0 and 1 are __neither__ prime _nor composite. A composite number may be written as the product of prime numbers. This product is the _ prime factorization of the number. Example 1 Find the prime factorization of 660. 660 Write the number as the product of two factors. 66 6 Continue to factor until only prime factors remain. The prime factorization of 660 is 2 10 11 2 5 3 2 · 2 · 3 · 5 · 11 = 2² · 3 · 5 · 11 The greatest of the factors common to TWO or more number is the greatest common factor (GCF). Example 2 Find the greatest common factor of 36 and 60. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 GCF = 6 Example 3 Find the greatest common factor of 90 and 120, using prime factorization. 90 9 3 3 120 10 2 12 5 6 2 10 2 5 90 = 2·3·3·5 = 120 = 2·2·2·3·5 = GCF = 2 · 3·5 = 2 3 Example 4 Write 1. Divide by GCF. 30 = 2 · 15 45 = 3 · 15 = in simplest form 2. Use prime factorization. = = 2 · 3² · 5 2³ · 3 · 5 30