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to Prime Factors in the Rust Track

Published at Jul 13 2020 · 0 comments
Test suite

Compute the prime factors of a given natural number.

A prime number is only evenly divisible by itself and 1.

Note that 1 is not a prime number.


What are the prime factors of 60?

  • Our first divisor is 2. 2 goes into 60, leaving 30.
  • 2 goes into 30, leaving 15.
    • 2 doesn't go cleanly into 15. So let's move on to our next divisor, 3.
  • 3 goes cleanly into 15, leaving 5.
    • 3 does not go cleanly into 5. The next possible factor is 4.
    • 4 does not go cleanly into 5. The next possible factor is 5.
  • 5 does go cleanly into 5.
  • We're left only with 1, so now, we're done.

Our successful divisors in that computation represent the list of prime factors of 60: 2, 2, 3, and 5.

You can check this yourself:

  • 2 * 2 * 3 * 5
  • = 4 * 15
  • = 60
  • Success!

Rust Installation

Refer to the exercism help page for Rust installation and learning resources.

Writing the Code

Execute the tests with:

$ cargo test

All but the first test have been ignored. After you get the first test to pass, open the tests source file which is located in the tests directory and remove the #[ignore] flag from the next test and get the tests to pass again. Each separate test is a function with #[test] flag above it. Continue, until you pass every test.

If you wish to run all ignored tests without editing the tests source file, use:

$ cargo test -- --ignored

To run a specific test, for example some_test, you can use:

$ cargo test some_test

If the specific test is ignored use:

$ cargo test some_test -- --ignored

To learn more about Rust tests refer to the online test documentation

Make sure to read the Modules chapter if you haven't already, it will help you with organizing your files.

Further improvements

After you have solved the exercise, please consider using the additional utilities, described in the installation guide, to further refine your final solution.

To format your solution, inside the solution directory use

cargo fmt

To see, if your solution contains some common ineffective use cases, inside the solution directory use

cargo clippy --all-targets

Submitting the solution

Generally you should submit all files in which you implemented your solution (src/lib.rs in most cases). If you are using any external crates, please consider submitting the Cargo.toml file. This will make the review process faster and clearer.

Feedback, Issues, Pull Requests

The exercism/rust repository on GitHub is the home for all of the Rust exercises. If you have feedback about an exercise, or want to help implement new exercises, head over there and create an issue. Members of the rust track team are happy to help!

If you want to know more about Exercism, take a look at the contribution guide.


The Prime Factors Kata by Uncle Bob http://butunclebob.com/ArticleS.UncleBob.ThePrimeFactorsKata

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.


use prime_factors::factors;

fn test_no_factors() {
    assert_eq!(factors(1), vec![]);

fn test_prime_number() {
    assert_eq!(factors(2), vec![2]);

fn test_square_of_a_prime() {
    assert_eq!(factors(9), vec![3, 3]);

fn test_cube_of_a_prime() {
    assert_eq!(factors(8), vec![2, 2, 2]);

fn test_product_of_primes_and_non_primes() {
    assert_eq!(factors(12), vec![2, 2, 3]);

fn test_product_of_primes() {
    assert_eq!(factors(901_255), vec![5, 17, 23, 461]);

fn test_factors_include_large_prime() {
    assert_eq!(factors(93_819_012_551), vec![11, 9539, 894_119]);
pub fn factors(n: u64) -> Vec<u64> {
    let primes = (2..=n).filter(is_prime);

    let mut result = Vec::new();
    let mut number = n;

    for prime in primes {
        while number % prime == 0 {
            result.push(prime); // prime is copied into the result
            number /= prime;
        // important "optimization" - without this we end up checking *every* number up to and including n for being prime
        // by exiting early, we only need to check numbers up to the largest prime factor
        if prime > number {

        // another important optimisation. This one helps in cases where a very large prime number is a factor, after each division we can check if the remainder is prime: if it is, we're done!
        // This actually slows down cases where n has many prime factors, but hopefully if there are lots of prime factors, they are all relatively small?
        if is_prime(&number) {
            result.push(number); // prime is copied into the result


// credit to SimSmith for his excellent solution:
// https://exercism.io/tracks/rust/exercises/nth-prime/solutions/c9e8c5f3f4244431bff6c317ace73175
// It's such a nice small function to pull in and use here
fn is_prime(n: &u64) -> bool {
    // Does not need to go higher than m = √n
    let limit = (*n as f32).sqrt() as u64;
    let is_divisor = |x| n % x == 0;

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drmason13's Reflection

Went for a solution that uses primes. Rust iterators are great! There laziness makes this feasible even for large prime factors; as long as checks for early exits are used the iterator ends up not doing nearly as much work as you might fear!