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

Example: 210

2^1 x 3^1 x 5^1 x 7^1 = 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.

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

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Q: How do you know if you have all factor pairs of a number?
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