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:
- Everything you ever wanted to know about Prime Numbers
- Prime factorization, and more fun – Factoring Trees
How to find the GCF of two numbers:
- 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!
- Multiply those factors both numbers have in common.
- 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!
18 = 2 x 3 x 3
24 = 2 x 2 x 2 x 3
Step 2: Now what’s common to these two?
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.
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