# To find Factors and Coprimes

Number system is a very important chapter and you can find good number of questions in various competitive exams. Important formulas are the following.

A number can be written in its prime factorization format. For example 100 = 2^{2} x 5^{2}

**Formula 1:** The number of factors of a number N is (p+1).(q+1).(r+1)... where N = a^{p} x b^{q} x c^{r} ...

Example: Find the number of factors of 100.

Ans: We know that 100 = 2^{2} x 5^{2}

So number of factors of 100 = (2 +1 ).(2 +1) = 9.

Infact the factors are 1, 2, 4, 5, 10, 20, 25, 50, 100

**Formula 2:** The sum of factors of a number N is \( \frac{{{a^{p + 1}} - 1}}{{a - 1}} \times \frac{{{b^{q + 1}} - 1}}{{b - 1}} \times \frac{{{c^{r + 1}} - 1}}{{c - 1}} \)

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