﻿ factors – Algosim documentation
Algosim documentation: factors

# factors

Factorises an integer, preferably into prime factors.

## Syntax

• `factors(n)`

• `n` is an integer

## Description

• If `n` is a positive integer greater than or equal to `2`, `factors(n)` is the unique sorted list of prime numbers whose product is `n`. The result is the same as `PrimeFactors(n)`.

• If `n = 1`, `factors(n) = '(1)`. (On the other hand, `PrimeFactors(1) = '()`.)

• If `n = 0`, `factors(n) = '(0)`.

• If `n` is a negative integer, `factors(n)` is the same list as `factors(abs(n))` but with the first element with a minus sign.

## Notes

Unlike `PrimeFactors`, `factors` is defined also for non-positive integers. Moreover, while `PrimeFactors(1)` is the empty list (the unique list of prime numbers whose product is `1`), `factors(1)` is `'(1)`. For positive integers greater than or equal to `2`, `PrimeFactors` and `factors` return the same list.

Unlike `PrimeFactors`, the elements of `factors(n)` might not be prime; indeed, `1`, `0`, and negative integers are not prime numbers.

## Examples

`factors(1)`
`1`
`factors(652358510)`
```2
5
17
3837403
```
`factors(6454824420)`
```2
2
3
5
11
23
53
71
113
```
`factors(4096)`
```2
2
2
2
2
2
2
2
2
2
2
2
```
`factors(362014271)`
`362014271`
`factors(0)`
`0`
`factors(−652358510)`
```−2
5
17
3837403
```