Given a positive integer N. The task is to check if N is an unusual number or not. Print ‘YES’ if M is an unusual number else print ‘NO’.
Unusual number : In Mathematics, an unusual number is a natural number whose greatest prime factor is strictly greater than square root of n.
The first few unusual numbers are –
2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 26, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 46, 47, 51
Examples:
Input : N = 14 Output : YES Explanation : 7 is largest prime factor of 14 and 7 is strictly greater than square root of 14 Input : N = 16 Output : NO Explanation : 2 is largest prime factor of 16 and 2 is less than square root of 16 ( i.e 4 ).
Approach :
- Find the largest prime factor of the given number N. To find the largest prime factor of N refer this .
- Check if the largest prime factor of N is strictly greater than square root of N.
- If ‘YES’ then N is an Unusual number otherwise Not.
Below is the implementation of the above approach:
C++
// C++ Program to check Unusual number #include <bits/stdc++.h> using namespace std; // Utility function to find largest // prime factor of a number int largestPrimeFactor(int n) { // Initialize the maximum prime factor // variable with the lowest one int max = -1; // Print the number of 2s that divide n while (n % 2 == 0) { max = 2; n >>= 1; // equivalent to n /= 2 } // n must be odd at this point, thus skip // the even numbers and iterate only for // odd integers for (int i = 3; i <= sqrt(n); i += 2) { while (n % i == 0) { max = i; n = n / i; } } // This condition is to handle the case // when n is a prime number greater than 2 if (n > 2) max = n; return max; } // Function to check Unusual number bool checkUnusual(int n) { // Get the largest Prime Factor // of the number int factor = largestPrimeFactor(n); // Check if largest prime factor // is greater than sqrt(n) if (factor > sqrt(n)) { return true; } else { return false; } } // Driver Code int main() { int n = 14; if (checkUnusual(n)) { cout << "YES" << "\n"; } else { cout << "NO" << "\n"; } return 0; } |
Java
// Java Program to check Unusual number class GFG { // Utility function to find largest // prime factor of a number static int largestPrimeFactor(int n) { // Initialize the maximum prime factor // variable with the lowest one int max = -1; // Print the number of 2s that divide n while (n % 2 == 0) { max = 2; n >>= 1; // equivalent to n /= 2 } // n must be odd at this point, thus skip // the even numbers and iterate only for // odd integers for (int i = 3; i <= Math.sqrt(n); i += 2) { while (n % i == 0) { max = i; n = n / i; } } // This condition is to handle the case // when n is a prime number greater than 2 if (n > 2) max = n; return max; } // Function to check Unusual number static boolean checkUnusual(int n) { // Get the largest Prime Factor // of the number int factor = largestPrimeFactor(n); // Check if largest prime factor // is greater than sqrt(n) if (factor > Math.sqrt(n)) { return true; } else { return false; } } // Driver Code public static void main(String[] args) { int n = 14; if (checkUnusual(n)) { System.out.println("YES"); } else { System.out.println("NO"); } }} |
Python3
# Python Program to check Unusual number from math import sqrt # Utility function to find largest # prime factor of a number def largestPrimeFactor(n): # Initialize the maximum prime factor # variable with the lowest one max = -1 # Print the number of 2s that divide n while n % 2 == 0: max = 2; n >>= 1; # equivalent to n /= 2 # n must be odd at this point, thus skip # the even numbers and iterate only for # odd integers for i in range(3,int(sqrt(n))+1,2): while n % i == 0: max = i; n = n / i; # This condition is to handle the case # when n is a prime number greater than 2 if n > 2: max = n return max # Function to check Unusual number def checkUnusual(n): # Get the largest Prime Factor # of the number factor = largestPrimeFactor(n) # Check if largest prime factor # is greater than sqrt(n) if factor > sqrt(n): return True else : return False # Driver Code if __name__ == '__main__': n = 14 if checkUnusual(n): print("YES") else: print("NO")# This code is contributed # by Harshit Saini |
C#
// C# Program to check Unusual number using System;class GFG { // Utility function to find largest // prime factor of a number static int largestPrimeFactor(int n) { // Initialize the maximum prime factor // variable with the lowest one int max = -1; // Print the number of 2s that divide n while (n % 2 == 0) { max = 2; n >>= 1; // equivalent to n /= 2 } // n must be odd at this point, thus skip // the even numbers and iterate only for // odd integers for (int i = 3; i <= Math.Sqrt(n); i += 2) { while (n % i == 0) { max = i; n = n / i; } } // This condition is to handle the case // when n is a prime number greater than 2 if (n > 2) max = n; return max; } // Function to check Unusual number static bool checkUnusual(int n) { // Get the largest Prime Factor // of the number int factor = largestPrimeFactor(n); // Check if largest prime factor // is greater than sqrt(n) if (factor > Math.Sqrt(n)) { return true; } else { return false; } } // Driver Code public static void Main() { int n = 14; if (checkUnusual(n)) { Console.WriteLine("YES"); } else { Console.WriteLine("NO"); } }} |
PHP
<?php// PHP Program to check Unusual number // Utility function to find largest // prime factor of a number function largestPrimeFactor($n) { // Initialize the maximum prime factor // variable with the lowest one $max = -1; // Print the number of 2s that divide n while ($n % 2 == 0) { $max = 2; $n >>= 1; // equivalent to n /= 2 } // n must be odd at this point, thus skip // the even numbers and iterate only for // odd integers for ($i = 3; $i <= sqrt($n); $i += 2) { while ($n % $i == 0) { $max = $i; $n = $n / $i; } } // This condition is to handle the case // when n is a prime number greater than 2 if ($n > 2) $max = $n; return $max; } // Function to check Unusual number function checkUnusual($n) { // Get the largest Prime Factor // of the number $factor = largestPrimeFactor($n); // Check if largest prime factor // is greater than sqrt(n) if ($factor > sqrt($n)) { return true; } else { return false; } } // Driver Code $n = 14; if (checkUnusual($n)) { echo "YES"."\n"; } else { echo "NO"."\n"; } // This code is contributed // by Harshit Saini ?> |
Javascript
<script>// javascript Program to check Unusual number // Utility function to find largest // prime factor of a number function largestPrimeFactor( n) { // Initialize the maximum prime factor // variable with the lowest one var max = -1; // Print the number of 2s that divide n while (n % 2 == 0) { max = 2; n >>= 1; // equivalent to n /= 2 } // n must be odd at this point, thus skip // the even numbers and iterate only for // odd integers for (var i = 3; i <= Math.sqrt(n); i += 2) { while (n % i == 0) { max = i; n = n / i; } } // This condition is to handle the case // when n is a prime number greater than 2 if (n > 2) max = n; return max; } // Function to check Unusual number function checkUnusual(n) { // Get the largest Prime Factor // of the number var factor = largestPrimeFactor(n); // Check if largest prime factor // is greater than sqrt(n) if (factor > Math.sqrt(n)) { return true; } else { return false; } } // Driver Code var n = 14; if (checkUnusual(n)) { document.write("YES"); } else { document.write("NO"); } </script> |
Output:
YES
Time complexity: 
Auxiliary space:
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