Solution: The GCF of 22 and 18 is 2
Methods
How to find the GCF of 22 and 18 using Prime Factorization
One way to find the GCF of 22 and 18 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 22?
What are the Factors of 18?
Here is the prime factorization of 22:
2
1
×
1
1
1
2^1 × 11^1
2 1 × 1 1 1
And this is the prime factorization of 18:
2
1
×
3
2
2^1 × 3^2
2 1 × 3 2
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 22 and 18 by multiplying all the matching prime factors to get a GCF of 22 and 18 as 4:
Thus, the GCF of 22 and 18 is: 4
How to Find the GCF of 22 and 18 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 22 and 18 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, 22 and 18:
Factors of 22: 1, 2, 11, 22
Factors of 18: 1, 2, 3, 6, 9, 18
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 22 and 18 would be 2.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 49 and 106?
What is the GCF of 77 and 92?
What is the GCF of 68 and 54?
What is the GCF of 80 and 47?
What is the GCF of 117 and 115?