// Finds the prime factors of a number in increasing order, with repetition.

pub fn prime_factors(n: u64) -> Vec<u64> {

let mut i = 2;

let mut n = n;

let mut factors = Vec::new();

while i * i <= n {

if n.is_multiple_of(i) {

n /= i;

factors.push(i);

} else {

if i != 2 {

i += 1;

}

i += 1;

}

}

if n > 1 {

factors.push(n);

}

factors

}

#[cfg(test)]

mod tests {

use super::*;

#[test]

fn it_works() {

assert_eq!(prime_factors(0), vec![]);

assert_eq!(prime_factors(1), vec![]);

assert_eq!(prime_factors(11), vec![11]);

assert_eq!(prime_factors(25), vec![5, 5]);

assert_eq!(prime_factors(33), vec![3, 11]);

assert_eq!(prime_factors(2560), vec![2, 2, 2, 2, 2, 2, 2, 2, 2, 5]);

}

}