Solution: The GCF of 99 and 66 is 33
Methods
How to find the GCF of 99 and 66 using Prime Factorization
One way to find the GCF of 99 and 66 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 99?
What are the Factors of 66?
Here is the prime factorization of 99:
3
2
×
1
1
1
3^2 × 11^1
3 2 × 1 1 1
And this 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
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 99 and 66 by multiplying all the matching prime factors to get a GCF of 99 and 66 as 1089:
Thus, the GCF of 99 and 66 is: 1089
How to Find the GCF of 99 and 66 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 99 and 66 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, 99 and 66:
Factors of 99: 1, 3, 9, 11, 33, 99
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 11, 33. Since 33 is the largest of these common factors, the GCF of 99 and 66 would be 33.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 122 and 7?
What is the GCF of 143 and 86?
What is the GCF of 139 and 90?
What is the GCF of 120 and 37?
What is the GCF of 79 and 113?