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

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Fini!

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