# Count of distinct power of prime factor of N

Given a positive integer **N**, the task is to find the total number of distinct power of prime factor of the given number N.**Examples:**

Input:N = 216Output:4Explanation:

216 can be expressed as 2 * 2^{2 }* 3 * 3^{2}.

The factors satisfying the conditions are 2, 2^{2}, 3 and 3^{2}as all of them are written as distinct positive powers of prime factors.Input:N = 24Output:3Explanation:

24 can be expressed as 2 * 2^{2}* 3

**Approach:** The idea is to find all the prime factors of N and how many times each prime factor divides **N**.

Suppose the prime factor **‘p’** divides N **‘z’** times, then the required distinct prime factors are **p, p ^{2}, …, p^{i}**.

To find the number of distinct primes factor for prime number p find the minimum value of i such that

**(1 + 2 + …. + i) â‰¤ z**.

Therefore, for each prime number dividing

**N**

**K**number of times, find the minimum value of i such that

**(1 + 2 + …. + i) â‰¤ K**.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to count the number` `// of distinct positive power of` `// prime factor of integer N` `int` `countFac(` `int` `n)` `{` ` ` `int` `m = n;` ` ` `int` `count = 0;` ` ` `// Iterate for all prime factor` ` ` `for` `(` `int` `i = 2; (i * i) <= m; ++i) {` ` ` `int` `total = 0;` ` ` `// If it is a prime factor,` ` ` `// count the total number` ` ` `// of times it divides n.` ` ` `while` `(n % i == 0) {` ` ` `n /= i;` ` ` `++total;` ` ` `}` ` ` `int` `temp = 0;` ` ` `// Find the Number of distinct` ` ` `// possible positive numbers` ` ` `for` `(` `int` `j = 1;` ` ` `(temp + j) <= total;` ` ` `++j) {` ` ` `temp += j;` ` ` `++count;` ` ` `}` ` ` `}` ` ` `if` `(n != 1)` ` ` `++count;` ` ` `// Return the final count` ` ` `return` `count;` `}` `// Driver Code` `int` `main()` `{` ` ` `// Given Number N` ` ` `int` `N = 24;` ` ` `// Function Call` ` ` `cout << countFac(N);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.util.*;` `class` `GFG{` `// Function to count the number` `// of distinct positive power of` `// prime factor of integer N` `static` `int` `countFac(` `int` `n)` `{` ` ` `int` `m = n;` ` ` `int` `count = ` `0` `;` ` ` `// Iterate for all prime factor` ` ` `for` `(` `int` `i = ` `2` `; (i * i) <= m; ++i)` ` ` `{` ` ` `int` `total = ` `0` `;` ` ` ` ` `// If it is a prime factor,` ` ` `// count the total number` ` ` `// of times it divides n.` ` ` `while` `(n % i == ` `0` `)` ` ` `{` ` ` `n /= i;` ` ` `++total;` ` ` `}` ` ` `int` `temp = ` `0` `;` ` ` ` ` `// Find the Number of distinct` ` ` `// possible positive numbers` ` ` `for` `(` `int` `j = ` `1` `; (temp + j) <= total; ++j)` ` ` `{` ` ` `temp += j;` ` ` `++count;` ` ` `}` ` ` `}` ` ` `if` `(n != ` `1` `)` ` ` `++count;` ` ` ` ` `// Return the final count` ` ` `return` `count;` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` ` ` `// Given Number N` ` ` `int` `N = ` `24` `;` ` ` `// Function Call` ` ` `System.out.println(countFac(N));` `}` `}` `// This code is contributed by Pratima Pandey` |

## Python3

`# Python3 program for the above approach` `# Function to count the number` `# of distinct positive power of` `# prime factor of integer N` `def` `countFac(n):` ` ` ` ` `m ` `=` `n` ` ` `count ` `=` `0` ` ` `# Iterate for all prime factor` ` ` `i ` `=` `2` ` ` `while` `((i ` `*` `i) <` `=` `m):` ` ` `total ` `=` `0` ` ` `# If it is a prime factor,` ` ` `# count the total number` ` ` `# of times it divides n.` ` ` `while` `(n ` `%` `i ` `=` `=` `0` `):` ` ` `n ` `/` `=` `i` ` ` `total ` `+` `=` `1` ` ` ` ` `temp ` `=` `0` ` ` `# Find the Number of distinct` ` ` `# possible positive numbers` ` ` `j ` `=` `1` ` ` `while` `((temp ` `+` `j) <` `=` `total):` ` ` `temp ` `+` `=` `j` ` ` `count ` `+` `=` `1` ` ` `j ` `+` `=` `1` ` ` ` ` `i ` `+` `=` `1` ` ` ` ` `if` `(n !` `=` `1` `):` ` ` `count ` `+` `=` `1` ` ` `# Return the final count` ` ` `return` `count` `# Driver Code` `# Given number N` `N ` `=` `24` `# Function call` `print` `(countFac(N))` `# This code is contributed by sanjoy_62` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG{` `// Function to count the number` `// of distinct positive power of` `// prime factor of integer N` `static` `int` `countFac(` `int` `n)` `{` ` ` `int` `m = n;` ` ` `int` `count = 0;` ` ` `// Iterate for all prime factor` ` ` `for` `(` `int` `i = 2; (i * i) <= m; ++i)` ` ` `{` ` ` `int` `total = 0;` ` ` ` ` `// If it is a prime factor,` ` ` `// count the total number` ` ` `// of times it divides n.` ` ` `while` `(n % i == 0)` ` ` `{` ` ` `n /= i;` ` ` `++total;` ` ` `}` ` ` `int` `temp = 0;` ` ` ` ` `// Find the Number of distinct` ` ` `// possible positive numbers` ` ` `for` `(` `int` `j = 1; (temp + j) <= total; ++j)` ` ` `{` ` ` `temp += j;` ` ` `++count;` ` ` `}` ` ` `}` ` ` `if` `(n != 1)` ` ` `++count;` ` ` ` ` `// Return the final count` ` ` `return` `count;` `}` `// Driver code` `public` `static` `void` `Main()` `{` ` ` ` ` `// Given Number N` ` ` `int` `N = 24;` ` ` `// Function Call` ` ` `Console.Write(countFac(N));` `}` `}` `// This code is contributed by Code_Mech` |

## Javascript

`<script>` `// Javascript program for the above approach` `// Function to count the number` `// of distinct positive power of` `// prime factor of integer N` `function` `countFac(n)` `{` ` ` `var` `m = n;` ` ` `var` `count = 0;` ` ` `// Iterate for all prime factor` ` ` `for` `(` `var` `i = 2; (i * i) <= m; ++i)` ` ` `{` ` ` `var` `total = 0;` ` ` ` ` `// If it is a prime factor,` ` ` `// count the total number` ` ` `// of times it divides n.` ` ` `while` `(n % i == 0)` ` ` `{` ` ` `n /= i;` ` ` `++total;` ` ` `}` ` ` `var` `temp = 0;` ` ` ` ` `// Find the Number of distinct` ` ` `// possible positive numbers` ` ` `for` `(` `var` `j = 1; (temp + j) <= total; ++j)` ` ` `{` ` ` `temp += j;` ` ` `++count;` ` ` `}` ` ` `}` ` ` `if` `(n != 1)` ` ` `++count;` ` ` ` ` `// Return the final count` ` ` `return` `count;` `}` `// Driver code` `// Given Number N` `var` `N = 24;` `// Function Call` `document.write(countFac(N));` `// This code is contributed by Khushboogoyal499` ` ` `</script>` |

**Output:**

3

**Time complexity:** *O(sqrt(N))*

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