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# MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

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MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

Lesson 9: Finding the Sum of the Factors of a Number

Example: What is the sum of the factors of 10,500?

From the prime factorization 22 x 31 x 53 x 71, we know 10,500 has 3 x 2 x 4 x 2 = 48 factors.

The sum of these 48 factors can be calculated from the prime factorization, too:

( )( )( )( )

(20 + 21 + 22)(30 + 31)(50 + 51 + 52 + 53)(70 + 71) = 7 × 4 × 156 × 8 = 34,944.

Fini!

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