1.2 KiB
prime-numbers-decomposition
Created by @theoludwig on 16 October 2021.
Instructions
Definition
In mathematics, product decomposition of prime factors (also known as integer factorization into prime numbers) involves writing a strictly positive integer as a product of prime numbers.
This factorization is unique and exists for all numbers and has many applications, particularly in RSA cryptography.
Note : A prime number is a natural integer which admits exactly two distinct positive divisors. (1 and itself). Example: 2, 3, 5, 7, 11, 13, 17, 19...
How to decompose a number into a product of factors of prime numbers?
To find the product decomposition of prime factors of a number N, there is no mathematical formula. To achieve this, there are algorithms, the most basic of which attempts to divide the number N by the set of prime factors p which are less than N.
If p is a divisor of N then start again by taking a new N = N / p as long as there are possible prime divisors.
Examples
Example
Input
32
Output
2 * 2 * 2 * 2 * 2
See the test folder for examples of input/output.