# Find the total number of composite factor for a given number

Given an integer N, the task is to find the total number of composite factors of N. Composite factors of a number are the factors which are not prime.

Examples:

Input: N = 24
Output: 5
1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24.
Out of which only 4, 6, 8, 12 and 24 are composites.

Input: N = 100
Output: 6

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• Find all the factors of N and store it in a variable totalFactors
• Find all the prime factors of N and store it in a variable primeFactors
• Now, total composite factors will be totalFactors – primeFactors – 1 (1 is subtracted because 1 is neither prime nor composite).

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the count ` `// of prime factors of n ` `int` `composite_factors(``int` `n) ` `{ ` `    ``int` `count = 0; ` `    ``int` `i, j; ` ` `  `    ``// Initialise array with 0 ` `    ``int` `a[n + 1] = { 0 }; ` `    ``for` `(i = 1; i <= n; ++i) { ` `        ``if` `(n % i == 0) { ` ` `  `            ``// Stored i value into an array ` `            ``a[i] = i; ` `        ``} ` `    ``} ` ` `  `    ``// Every non-zero value at a[i] denotes ` `    ``// that i is a factor of n ` `    ``for` `(i = 2; i <= n; i++) { ` `        ``j = 2; ` `        ``int` `p = 1; ` ` `  `        ``// Find if i is prime ` `        ``while` `(j < a[i]) { ` `            ``if` `(a[i] % j == 0) { ` `                ``p = 0; ` `                ``break``; ` `            ``} ` `            ``j++; ` `        ``} ` ` `  `        ``// If i is a factor of n ` `        ``// and i is not prime ` `        ``if` `(p == 0 && a[i] != 0) { ` `            ``count++; ` `        ``} ` `    ``} ` ` `  `    ``return` `count; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 100; ` ` `  `    ``cout << composite_factors(n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `Gfg  ` `{  ` ` `  `// Function to return the count ` `// of prime factors of n ` `public` `static` `int` `composite_factors(``int` `n) ` `{ ` `    ``int` `count = ``0``; ` `    ``int` `i, j; ` ` `  `    ``// Initialise array with 0 ` `    ``int``[] a=``new` `int``[n+``1``]; ` `    ``for``( i = ``0``; i < n; i++) ` `    ``{ ` `        ``a[i]=``0``; ` `    ``} ` `    ``for` `(i = ``1``; i <= n; ++i)  ` `    ``{ ` `        ``if` `(n % i == ``0``) ` `        ``{ ` ` `  `            ``// Stored i value into an array ` `            ``a[i] = i; ` `        ``} ` `    ``} ` ` `  `    ``// Every non-zero value at a[i] denotes ` `    ``// that i is a factor of n ` `    ``for` `(i = ``2``; i <= n; i++)  ` `    ``{ ` `        ``j = ``2``; ` `        ``int` `p = ``1``; ` ` `  `        ``// Find if i is prime ` `        ``while` `(j < a[i])  ` `        ``{ ` `            ``if` `(a[i] % j == ``0``)  ` `            ``{ ` `                ``p = ``0``; ` `                ``break``; ` `            ``} ` `            ``j++; ` `        ``} ` ` `  `        ``// If i is a factor of n ` `        ``// and i is not prime ` `        ``if` `(p == ``0` `&& a[i] != ``0``)  ` `        ``{ ` `            ``count++; ` `        ``} ` `     `  `} ` `    ``return` `count; ` `} ` ` `  ` `  `// Driver code ` `public` `static` `void` `main(String[] args)  ` `{  ` `    ``int` `n = ``100``; ` `     `  `    ``System.out.println(composite_factors(n)); ` ` `  `} ` `} ` ` `  `// This code is contributed by nidhi16bcs2007 `

## Python3

 `# Python3 implementation of the approach  ` ` `  `# Function to return the count  ` `# of prime factors of n  ` `def` `composite_factors(n) :  ` ` `  `    ``count ``=` `0``; ` `     `  `    ``# Initialise array with 0 ` `    ``a ``=` `[``0``]``*``(n ``+` `1``) ; ` `     `  `    ``for` `i ``in` `range``(``1``, n ``+` `1``) :  ` `        ``if` `(n ``%` `i ``=``=` `0``) : ` ` `  `            ``# Stored i value into an array  ` `            ``a[i] ``=` `i; ` ` `  `    ``# Every non-zero value at a[i] denotes  ` `    ``# that i is a factor of n  ` `    ``for` `i ``in` `range``(``2``,n ``+` `1``) : ` `        ``j ``=` `2``;  ` `        ``p ``=` `1``;  ` ` `  `        ``# Find if i is prime  ` `        ``while` `(j < a[i]) : ` `            ``if` `(a[i] ``%` `j ``=``=` `0``) : ` `                ``p ``=` `0``;  ` `                ``break``;  ` `                 `  `            ``j ``+``=` `1``;  ` ` `  ` `  `        ``# If i is a factor of n  ` `        ``# and i is not prime  ` `        ``if` `(p ``=``=` `0` `and` `a[i] !``=` `0``) : ` `            ``count ``+``=` `1``;  ` ` `  `    ``return` `count;  ` ` `  ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `: ` ` `  `    ``n ``=` `100``;  ` ` `  `    ``print``(composite_factors(n));  ` `     `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to return the count ` `// of prime factors of n ` `static` `int` `composite_factors(``int` `n) ` `{ ` `    ``int` `count = 0; ` `    ``int` `i, j; ` ` `  `    ``// Initialise array with 0 ` `    ``int``[] a = ``new` `int``[n + 1]; ` `    ``for``( i = 0; i < n; i++) ` `    ``{ ` `        ``a[i]=0; ` `    ``} ` `    ``for` `(i = 1; i <= n; ++i) ` `    ``{ ` `        ``if` `(n % i == 0) ` `        ``{ ` ` `  `            ``// Stored i value into an array ` `            ``a[i] = i; ` `        ``} ` `    ``} ` ` `  `    ``// Every non-zero value at a[i] denotes ` `    ``// that i is a factor of n ` `    ``for` `(i = 2; i <= n; i++) ` `    ``{ ` `        ``j = 2; ` `        ``int` `p = 1; ` ` `  `        ``// Find if i is prime ` `        ``while` `(j < a[i]) ` `        ``{ ` `            ``if` `(a[i] % j == 0) ` `            ``{ ` `                ``p = 0; ` `                ``break``; ` `            ``} ` `            ``j+=1; ` `        ``} ` ` `  `        ``// If i is a factor of n ` `        ``// and i is not prime ` `        ``if` `(p == 0 && a[i] != 0) ` `        ``{ ` `            ``count += 1; ` `        ``} ` ` `  `} ` `    ``return` `count; ` `} ` ` `  ` `  `// Driver code ` `public` `static` `void` `Main() ` `{ ` `    ``int` `n = 100; ` ` `  `    ``Console.WriteLine(composite_factors(n)); ` `} ` `} ` ` `  `// This code is contributed by mohit kumar 29 `

Output:

```6
```

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