CAT4MBA

Let N = a^m x bⁿ x c^p x . . .    

1. Number of divisors of any natural number N is (m+1) (n+1) (p+1)

 Example: 63504 = 7² x 2⁴ x 3⁴

So the number of divisors of 63504 = (2+1) (4+1) (4+1) = 75

Remember this includes the number 63504 and 1 also.

2. Number of even divisors = Number of divisors which are even.

Let N = 2^m x bⁿ x c^p x d^q x . . .    

Then number of even divisors = m (n+1) (p+1) (q+1)

Number of even divisors = 4 x 5 x 3 = 60

3. Number of odd divisors = Number of divisors which are odd

It’s same as calculating number of divisors of the number with out all the powers of 2.

For 63504, number of odd divisors = 3 x 5 = 15

4. Sum of all the divisors of a natural number N is 

                                [(a^m+1 -1) x (bⁿ⁺¹ -1) x (c^p+1 – 1)] / (a –1) (b –1) (c –1)

5. Product of the divisors of a natural number N is

                                                               N^x/2 where x = (m+1)(n+1)(p+1)