Total number of divisors for a given number | CPP program for finding number of divisor ; program for finding no . of divisors ; sieve method for prime calculation ; Traversing through all prime numbers ; calculate number of divisor with formula total div = ( p1 + 1 ) * ( p2 + 1 ) * ... . . * ( pn + 1 ) where n = ( a1 ^ p1 ) * ( a2 ^ p2 ) . ... * ( an ^ pn ) ai being prime divisor for n and pi are their respective power in factorization ; driver program
#include <bits/stdc++.h> NEW_LINE using namespace std ; int divCount ( int n ) { bool hash [ n + 1 ] ; memset ( hash , true , sizeof ( hash ) ) ; for ( int p = 2 ; p * p < n ; p ++ ) if ( hash [ p ] == true ) for ( int i = p * 2 ; i < n ; i += p ) hash [ i ] = false ; int total = 1 ; for ( int p = 2 ; p <= n ; p ++ ) { if ( hash [ p ] ) { int count = 0 ; if ( n % p == 0 ) { while ( n % p == 0 ) { n = n / p ; count ++ ; } total = total * ( count + 1 ) ; } } } return total ; } int main ( ) { int n = 24 ; cout << divCount ( n ) ; return 0 ; }