Concept Of Factors

Concept of Factors:
N = P^a * Q^b * R^c (Where P,Q and R are prime numbers and a, b and c are natural numbers)
Then
1. Total no of factors of N = (a+1)*(b+1)*(c+1)
2. Total no of perfect square factors of N= (a+1)/2 * (b/2+1) *(c+1)/2 [If a and c is an odd no, b is an even no]
3. Total no of odd factors of N= (1 * (b+1)*(c+1)) [If P=2]
4. Total no of odd factors of N= (a+1)*(b+1)*(c+1) [If 2 is not the factor of N]
5. Total no of even factors of N= (a * (b+1)*(c+1)) [If P=2]
6. Total no of even factors of N= 0 [If 2 is not the factor of N]
7. Total no of non ordered pairs of (x,y) such that (x * y = N) = [(a+1)*(b+1)*(c+1)]/2 note : If total no of factors is an even no.
8. Total no of non ordered pairs of (x,y) such that (x * y = N) = [(a+1)*(b+1)*(c+1)+ 1]/2 note : If total no of factors is an odd no.
9. Total no of co-prime pairs using all the factors of N = a+b+c+2 (ab+bc+ca) + 4abc
10. Sum of all the factors of N = [(P^(a+1) – 1)/(p – 1)] * [(Q^(b+1) – 1)/(Q – 1)] * [(R^(c+1) – 1)/(R – 1)]