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Prime Factors

# Prime Factors

Medium

## Instructions

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.

### Example

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!

### Running and testing your solutions

#### From the command line

Simply type `make chez` if you're using ChezScheme or `make guile` if you're using GNU Guile. Sometimes the name for the scheme binary on your system will differ from the defaults. When this is the case, you'll need to tell make by running `make chez chez=your-chez-binary` or `make guile guile=your-guile-binary`.

#### From a REPL

• Enter `(load "test.scm")` at the repl prompt.
• Develop your solution in `prime-factors.scm` reloading as you go.
• Run `(test)` to check your solution.

#### Failed Test Cases

If some of the test cases fail, you should see the failing input and the expected output. The failing input is presented as a list because the tests call your solution by `(apply prime-factors input-list)`. To learn more about `apply` see The Scheme Programming Language -- Chapter 5

### Source

The Prime Factors Kata by Uncle Bob
Edit via GitHub