Prime Factors

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!