How to find the number of Positive Divisors of a Number?

Let N be the number.

Now express N as the product of Prime factors

N=P₁^A1 * P₂^A2 * P₃^A3 * .........       

(Where P_i are the primes 
              Aj are the powers of respective primes,

              i =1,2,3....   and   j= 1,2,3...)

Let  τ(N) denote the number of positive divisors of n, then

τ(N)= (A1 +1) (A2 +1) (A3 +1)......

Example 1:

Find the number of positive divisors of 108.

Here N=108 

→Now write the number as the product of prime factors.

So 108 can be written as

108=2²×3³

The number of positive divisors of 108 is 

τ(108)= (2+1)(3+1) = 3×4 = 12   

    

Example 2:

Find the number of positive divisors of 50000.

Let N=50000

 50000 =2⁴×5⁵

The number of positive divisors of 108 is

τ(50000) = (4+1)(5+1) = 5×6 =30


              
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