How to Find the Number of Factors in a Number


This can be explained much better through an example.

Ex. How many factors are there in 1200 ?
Sol:- The proper factors of 1200 are 2,3,5.
1200= {2^4}{3^1}{5²}
That is, 2^p .3^q .5^r is a factor of 1200 where the values of p=0,1,2,3,4 ; q=0,1 ; r=0,1,2.
So, Total number of factors=5*2*3=30.
Since 2^0 =3^0 * 5^0 is also included among these factors.

Hence the required number of factors=30-1=29.