Given a number n, we need to find the product of all of its unique prime factors. Prime factors: It is basically a factor of the number that is a prime number itself.
Examples:
Input: num = 10 Output: Product is 10 Explanation: Here, the input number is 10 having only 2 prime factors and they are 5 and 2. And hence their product is 10. Input : num = 25 Output: Product is 5 Explanation: Here, for the input to be 25 we have only one unique prime factor i.e 5. And hence the required product is 5.
Method 1 (Simple)
Using a loop from i = 2 to n and check if i is a factor of n then check if i is prime number itself if yes then store product in product variable and continue this process till i = n.
// Java program to find product of // unique prime factors of a number. public class GFG {
public static long productPrimeFactors( int n)
{
long product = 1 ;
for ( int i = 2 ; i <= n; i++) {
// Checking if 'i' is factor of num
if (n % i == 0 ) {
// Checking if 'i' is a Prime number
boolean isPrime = true ;
for ( int j = 2 ; j <= i / 2 ; j++) {
if (i % j == 0 ) {
isPrime = false ;
break ;
}
}
// condition if 'i' is Prime number
// as well as factor of num
if (isPrime) {
product = product * i;
}
}
}
return product;
}
public static void main(String[] args)
{
int n = 44 ;
System.out.print(productPrimeFactors(n));
}
} // Contributed by _omg |
22
Method 2 (Efficient)
The idea is based on Efficient program to print all prime factors of a given number
// Java program to find product of // unique prime factors of a number. import java.util.*;
import java.lang.*;
public class GFG {
public static long productPrimeFactors( int n)
{
long product = 1 ;
// Handle prime factor 2 explicitly so that
// can optimally handle other prime factors.
if (n % 2 == 0 ) {
product *= 2 ;
while (n % 2 == 0 )
n = n / 2 ;
}
// n must be odd at this point. So we can
// skip one element (Note i = i +2)
for ( int i = 3 ; i <= Math.sqrt(n); i = i + 2 ) {
// While i divides n, print i and
// divide n
if (n % i == 0 ) {
product = product * i;
while (n % i == 0 )
n = n / i;
}
}
// This condition is to handle the case when n
// is a prime number greater than 2
if (n > 2 )
product = product * n;
return product;
}
public static void main(String[] args)
{
int n = 44 ;
System.out.print(productPrimeFactors(n));
}
} // Contributed by _omg |
22
Please refer complete article on Product of unique prime factors of a number for more details!