Prime Factorization

Prime factorization is a method used to break down an integer into its prime factors. A prime factor is a Prime Numbers that divides evenly into a given number.

To factor an integer into its prime factors, you start by dividing it by prime numbers until you can no longer do so. You usually want to start with the smallest possible primes, but there is no requirement to do so.

For example, let's say we want to find the prime factorization of 24:

  1. Divide by 2:

  2. Divide by 2 again:

  1. Divide by 2 once more:

Notice that we are left with a prime number: 3
We can see that and all 4 of these factors are prime!
So, the prime factorization of 24 is or more properly, .

Prime Factorization Trees

A prime factorization tree is a visual way to factor numbers into their primes. It is basically just a visual representation of the process we did above. Here you can see the primes have been colored

PFT 24 24 12 12 24->12 2_1 2 24->2_1 6 6 12->6 2_2 2 12->2_2 3 3 6->3 2_3 2 6->2_3
Note

Remember that only Composite Numbers can be factored into primes.