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Check if all Prime factors of number N are unique or not
• Last Updated : 16 Apr, 2020

Given a number N. The task is to check whether the given number N has unique prime factors or not. If yes then print YES else print NO.

Examples:

Input: N = 30
Output: YES
Explanation:
N = 30 = 2*3*5
As all the prime factors of 30 are unique.

Input: N = 100
Output: NO
Explanation:
N = 100 = 2*2*5*5
As all the prime factors of 100 are not unique because 2 and 5 are repeated twice.

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

Approach:

1. Find all the prime factors of the given number N using Sieve Of Eratosthenes.
2. If the product of all the prime factors obtained is equals to N then all prime factors are unique, so print YES.
3. Else print NO.

Below is the implementation of the above approach:

## CPP

 `// C++ program for the above approach``#include ``using` `namespace` `std;`` ` `// Function that returns the all the``// distinct prime factors in a vector``vector<``int``> primeFactors(``int` `n)``{``    ``int` `i, j;``    ``vector<``int``> Prime;`` ` `    ``// If n is divisible by 2``    ``if` `(n % 2 == 0) {``        ``Prime.push_back(2);``    ``}`` ` `    ``// Divide n till all factors of 2``    ``while` `(n % 2 == 0) {``        ``n = n / 2;``    ``}`` ` `    ``// Check for the prime numbers other``    ``// than 2``    ``for` `(i = 3; i <= ``sqrt``(n); i = i + 2) {`` ` `        ``// Store i in Prime[] i is a``        ``// factor of n``        ``if` `(n % i == 0) {``            ``Prime.push_back(i);``        ``}`` ` `        ``// Divide n till all factors of i``        ``while` `(n % i == 0) {``            ``n = n / i;``        ``}``    ``}`` ` `    ``// If n is greter than 2, then n is``    ``// prime number after n divided by``    ``// all factors``    ``if` `(n > 2) {``        ``Prime.push_back(n);``    ``}`` ` `    ``// Returns the vector Prime``    ``return` `Prime;``}`` ` `// Function that check whether N is the``// product of distinct prime factors``// or not``void` `checkDistinctPrime(``int` `n)``{``    ``// Returns the vector to store``    ``// all the distinct prime factors``    ``vector<``int``> Prime = primeFactors(n);`` ` `    ``// To find the product of all``    ``// distinct prime factors``    ``int` `product = 1;`` ` `    ``// Find the product``    ``for` `(``auto` `i : Prime) {``        ``product *= i;``    ``}`` ` `    ``// If product is equals to N,``    ``// print YES, else print NO``    ``if` `(product == n)``        ``cout << ``"YES"``;``    ``else``        ``cout << ``"NO"``;``}`` ` `// Driver Code``int` `main()``{``    ``int` `N = 30;``    ``checkDistinctPrime(N);``    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;`` ` `class` `GFG{``  ` `// Function that returns the all the``// distinct prime factors in a vector``static` `Vector primeFactors(``int` `n)``{``    ``int` `i, j;``    ``Vector Prime = ``new` `Vector();``  ` `    ``// If n is divisible by 2``    ``if` `(n % ``2` `== ``0``) {``        ``Prime.add(``2``);``    ``}``  ` `    ``// Divide n till all factors of 2``    ``while` `(n % ``2` `== ``0``) {``        ``n = n / ``2``;``    ``}``  ` `    ``// Check for the prime numbers other``    ``// than 2``    ``for` `(i = ``3``; i <= Math.sqrt(n); i = i + ``2``) {``  ` `        ``// Store i in Prime[] i is a``        ``// factor of n``        ``if` `(n % i == ``0``) {``            ``Prime.add(i);``        ``}``  ` `        ``// Divide n till all factors of i``        ``while` `(n % i == ``0``) {``            ``n = n / i;``        ``}``    ``}``  ` `    ``// If n is greter than 2, then n is``    ``// prime number after n divided by``    ``// all factors``    ``if` `(n > ``2``) {``        ``Prime.add(n);``    ``}``  ` `    ``// Returns the vector Prime``    ``return` `Prime;``}``  ` `// Function that check whether N is the``// product of distinct prime factors``// or not``static` `void` `checkDistinctPrime(``int` `n)``{``    ``// Returns the vector to store``    ``// all the distinct prime factors``    ``Vector Prime = primeFactors(n);``  ` `    ``// To find the product of all``    ``// distinct prime factors``    ``int` `product = ``1``;``  ` `    ``// Find the product``    ``for` `(``int` `i : Prime) {``        ``product *= i;``    ``}``  ` `    ``// If product is equals to N,``    ``// print YES, else print NO``    ``if` `(product == n)``        ``System.out.print(``"YES"``);``    ``else``        ``System.out.print(``"NO"``);``}``  ` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `N = ``30``;``    ``checkDistinctPrime(N);``}``}`` ` `// This code is contributed by sapnasingh4991`

## Python3

 `# Python3 program for the above approach `` ` `# Function that returns the all the ``# distinct prime factors in a vector ``def` `primeFactors(n) : `` ` `    ``Prime ``=` `[]; `` ` `    ``# If n is divisible by 2 ``    ``if` `(n ``%` `2` `=``=` `0``) :``        ``Prime.append(``2``); `` ` `    ``# Divide n till all factors of 2 ``    ``while` `(n ``%` `2` `=``=` `0``) :``        ``n ``=` `n ``/``/` `2``; ``     ` `    ``# Check for the prime numbers other ``    ``# than 2 ``    ``for` `i ``in` `range``(``3``, ``int``(n ``*``*` `(``1``/``2``)),``2``) :`` ` `        ``# Store i in Prime[] i is a ``        ``# factor of n ``        ``if` `(n ``%` `i ``=``=` `0``) :``            ``Prime.append(i); ``         ` `        ``# Divide n till all factors of i ``        ``while` `(n ``%` `i ``=``=` `0``) :``            ``n ``=` `n ``/``/` `i; `` ` `    ``# If n is greter than 2, then n is ``    ``# prime number after n divided by ``    ``# all factors ``    ``if` `(n > ``2``) :``        ``Prime.append(n); `` ` `    ``# Returns the vector Prime ``    ``return` `Prime; `` ` `# Function that check whether N is the ``# product of distinct prime factors ``# or not ``def` `checkDistinctPrime(n) : `` ` `    ``# Returns the vector to store ``    ``# all the distinct prime factors ``    ``Prime ``=` `primeFactors(n);``     ` `    ``# To find the product of all``    ``# distinct prime factors``    ``product ``=` `1``; `` ` `    ``# Find the product ``    ``for` `i ``in` `Prime :``        ``product ``*``=` `i; `` ` `    ``# If product is equals to N, ``    ``# print YES, else print NO ``    ``if` `(product ``=``=` `n) :``        ``print``(``"YES"``); ``    ``else` `:``        ``print``(``"NO"``); `` ` `# Driver Code ``if` `__name__ ``=``=` `"__main__"` `: `` ` `    ``N ``=` `30``; ``    ``checkDistinctPrime(N); `` ` `# This code is contributed by Yash_R`

## C#

 `// C# program for the above approach``using` `System;``using` `System.Collections.Generic;`` ` `class` `GFG{``   ` `// Function that returns the all the``// distinct prime factors in a vector``static` `List<``int``> primeFactors(``int` `n)``{``    ``int` `i;``    ``List<``int``> Prime = ``new` `List<``int``>();``   ` `    ``// If n is divisible by 2``    ``if` `(n % 2 == 0) {``        ``Prime.Add(2);``    ``}``   ` `    ``// Divide n till all factors of 2``    ``while` `(n % 2 == 0) {``        ``n = n / 2;``    ``}``   ` `    ``// Check for the prime numbers other``    ``// than 2``    ``for` `(i = 3; i <= Math.Sqrt(n); i = i + 2) {``   ` `        ``// Store i in Prime[] i is a``        ``// factor of n``        ``if` `(n % i == 0) {``            ``Prime.Add(i);``        ``}``   ` `        ``// Divide n till all factors of i``        ``while` `(n % i == 0) {``            ``n = n / i;``        ``}``    ``}``   ` `    ``// If n is greter than 2, then n is``    ``// prime number after n divided by``    ``// all factors``    ``if` `(n > 2) {``        ``Prime.Add(n);``    ``}``   ` `    ``// Returns the vector Prime``    ``return` `Prime;``}``   ` `// Function that check whether N is the``// product of distinct prime factors``// or not``static` `void` `checkDistinctPrime(``int` `n)``{``    ``// Returns the vector to store``    ``// all the distinct prime factors``    ``List<``int``> Prime = primeFactors(n);``   ` `    ``// To find the product of all``    ``// distinct prime factors``    ``int` `product = 1;``   ` `    ``// Find the product``    ``foreach` `(``int` `i ``in` `Prime) {``        ``product *= i;``    ``}``   ` `    ``// If product is equals to N,``    ``// print YES, else print NO``    ``if` `(product == n)``        ``Console.Write(``"YES"``);``    ``else``        ``Console.Write(``"NO"``);``}``   ` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `N = 30;``    ``checkDistinctPrime(N);``}``}`` ` `// This code is contributed by sapnasingh4991`
Output:
```YES
```

Time Complexity: O(N*log(log N)), where N is the given number.

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