Find Values of P and Q Satisfying the Equation N = P^2.Q

In this tutorial, we will explore how to determine values of P and Q satisfying the given equation.

A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first few prime numbers. Composite numbers are those that have more than two components. Neither prime nor composite, number one.

The goal is to determine P and Q that satisfy the expression N = P^2.Q, where P and Q are prime numbers, provided a number N(1 ≤ N ≤ 9×1018). P and Q must be prime numbers.

Instances:

The execution of the aforementioned concept is shown below:

C++ Program:

Output 1

(If we input the value of N as 2023)

Put a value of N: 2023 P is 17 Q is 7 

Output 2

(If we input the value of N as 175)

Put a value of N: 175 P is 5 Q is 7 

Output 3

(If we input the value of N as 158)

Put a value of N: 158 P is 9 Q is 2 

Output 4

(If we input the value of N as 254)

Put a value of N: 254 P is 11 Q is 2 

We can also write the above approach in javascript.

Javascript Code:

Program 1:

Output

P is 17 Q is 7 

Program 2:

Output

P is 5 Q is 7 

• Time Complexity will be O(³√n).
• Auxiliary space will be O(1).

So that's the end of the article. I sincerely hope you find this post to be educational and useful.