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MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 9: Finding the Sum of the Factors of a Number.

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Presentation on theme: "MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 9: Finding the Sum of the Factors of a Number."— Presentation transcript:

1 MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

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

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

4 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.

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

6 (2 0 + 2 1 + 2 2 )(3 0 + 3 1 )(5 0 + 5 1 + 5 2 + 5 3 )(7 0 + 7 1 )

7 (2 0 + 2 1 + 2 2 )(3 0 + 3 1 )(5 0 + 5 1 + 5 2 + 5 3 )(7 0 + 7 1 ) = 7 × 4 × 156 × 8 = 34,944.

8 Fini!


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