Prime Factors

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

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Source

The Prime Factors Kata by Uncle Bob