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37 lines
1.2 KiB
Markdown
37 lines
1.2 KiB
Markdown
# prime-numbers-decomposition
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Created by [@Divlo](https://github.com/Divlo) on 16 October 2021.
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## Instructions
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## Definition
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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.
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This factorization is unique and exists for all numbers and has many applications, particularly in RSA cryptography.
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**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...
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## How to decompose a number into a product of factors of prime numbers?
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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`.
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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.
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## Examples
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### Example
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#### Input
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```txt
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32
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```
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#### Output
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```txt
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2 * 2 * 2 * 2 * 2
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```
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See the `test` folder for examples of input/output.
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