The work that Ryan did to find the greatest common factor of 48 and 72 is as follows Prime factorization of 48 : 2 times 2 times 2 times 2 times 3 Prime factorization of 72 : 2 times 2 times 2 times 3 times 3 The greatest common factor is 2 times 2 times 2 times 3 times 3 What is Ryan’s error?

The prime factorizations are correct, but the GCF can use each common prime factor only as many times as it appears in both numbers. The factorizations share three 2s and one 3, so the GCF is 2 × 2 × 2 × 3 = 24. Ryan included an extra 3, which is not common to both factorizations. Therefore, his error was not including only common prime factors.

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