To find Factors and Coprimes

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 = 22 x 52 

Formula 1: The number of factors of a number N is (p+1).(q+1).(r+1)... where N = ap x bq x cr ...
 

Example: Find the number of factors of 100.  
Ans: We know that 100 = 22 x 52
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 \( \frac{{{a^{p + 1}} - 1}}{{a - 1}} \times \frac{{{b^{q + 1}} - 1}}{{b - 1}} \times \frac{{{c^{r + 1}} - 1}}{{c - 1}} \)