Solution: The GCF of 18 and 12 is 6
Methods
How to find the GCF of 18 and 12 using Prime Factorization
One way to find the GCF of 18 and 12 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 18?
What are the Factors of 12?
Here is the prime factorization of 18:
2
1
×
3
2
2^1 × 3^2
2 1 × 3 2
And this is the prime factorization of 12:
2
2
×
3
1
2^2 × 3^1
2 2 × 3 1
When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 18 and 12 by multiplying all the matching prime factors to get a GCF of 18 and 12 as 36:
Thus, the GCF of 18 and 12 is: 36
How to Find the GCF of 18 and 12 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 18 and 12 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.
Let’s take a look at the factors for each of these numbers, 18 and 12:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 12: 1, 2, 3, 4, 6, 12
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6. Since 6 is the largest of these common factors, the GCF of 18 and 12 would be 6.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 62 and 83?
What is the GCF of 46 and 148?
What is the GCF of 87 and 122?
What is the GCF of 120 and 49?
What is the GCF of 80 and 42?