Skip to content
Home » Blog » Greatest Common Factors (GCF)

Greatest Common Factors (GCF)

The greatest common factor, or GCF, is the greatest number that is a factor of two or more numbers.It’s also known sometimes as Highest Common Factor or HCF.

Quick Review on Prime Numbers and Factoring Trees:

Before we deep-dive into GCF – if you haven’t already, I would highly recommend these 2 lessons first, in this order:

  1. Everything you ever wanted to know about Prime Numbers
  2. Prime factorization, and more fun – Factoring Trees

How to find the GCF of two numbers:

  1. List the prime factors of each number. Use a factoring tree, they’re more fun and you’ll be less likely to make a mistake!
  2. Multiply those factors both numbers have in common.
  3. What if there are no common prime factors? Then, the GCF is 1.

Ready for some examples?

Example 1: Let’s start with an easy one. Find the GCF of 18 and 24.

Step 1: Have fun with some factor trees!

Factor trees for 18 and 24

18 = 2 x 3 x 3

24 = 2 x 2 x 2 x 3

Step 2: Now what’s common to these two?

Common factors of 18 and 24

As you can see, two factors are common – 2 and 3.

Step 3: Multiply them! 2 x 3 = 6

So, the greatest common factor of 18 and 24: GCF(18, 24)  = 6.

Example 2: Try finding the GCF or HCF of 3 numbers now. Find the GCF of 45, 60 and 90.

Step 1: Again, factor trees – 3 trees this time!

  • 45 = 3 x 3 x 5
  • 60 = 2 x 2 x 3 x 5
  • 90 = 2 x 3 x 3 x 5

Step 2: Now what’s common to these three numbers’ factors?

3 and 5 are common to all three numbers, right?

Step 3: Multiply them! 3 x 5 = 15

So, the greatest common factor of 45, 60 and 90:  GCF (45, 60, 90)  = 15.

Latest posts by Divya Pochimcherla (see all)