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If you know the prime factorization of a number, you can find out the total number of factors.

Example: 210

21 x 31 x 51 x 71 = 210

Add one to the exponents and multiply them.

2 x 2 x 2 x 2 = 16, the total number of factors.

You know that 1, 2, 3, 5, and 7 are factors. You need three more to get halfway.

2 x 3 = 6

2 x 5 = 10

2 x 7 = 14

Divide all those numbers into 210.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

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10y ago
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12y ago

Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Combine the factors, eliminating duplicates.

2 x 3 x 5 x 7 = 210, the LCM

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Q: How do you use prime factorization to find factors?
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