Solution: The GCF of 66 and 22 is 22
Methods
How to find the GCF of 66 and 22 using Prime Factorization
One way to find the GCF of 66 and 22 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 66?
What are the Factors of 22?
Here is the prime factorization of 66:
2
1
×
3
1
×
1
1
1
2^1 × 3^1 × 11^1
2 1 × 3 1 × 1 1 1
And this is the prime factorization of 22:
2
1
×
1
1
1
2^1 × 11^1
2 1 × 1 1 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 66 and 22 by multiplying all the matching prime factors to get a GCF of 66 and 22 as 484:
Thus, the GCF of 66 and 22 is: 484
How to Find the GCF of 66 and 22 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 66 and 22 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, 66 and 22:
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 22: 1, 2, 11, 22
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 11, 22. Since 22 is the largest of these common factors, the GCF of 66 and 22 would be 22.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 9 and 132?
What is the GCF of 62 and 28?
What is the GCF of 32 and 150?
What is the GCF of 35 and 6?
What is the GCF of 53 and 18?