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MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

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

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

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From the prime factorization 2 2 x 3 1 x 5 3 x 7 1, we know 10,500 has 3 x 2 x 4 x 2 = 48 factors.

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

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( )( )( )( )

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( )( )( )( ) = 7 × 4 × 156 × 8 = 34,944.

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Fini!

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