Solution: The GCF of 33 and 99 is 33
Methods
How to find the GCF of 33 and 99 using Prime Factorization
One way to find the GCF of 33 and 99 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 33?
What are the Factors of 99?
Here is the prime factorization of 33:
3
1
×
1
1
1
3^1 × 11^1
3 1 × 1 1 1
And this is the prime factorization of 99:
3
2
×
1
1
1
3^2 × 11^1
3 2 × 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 33 and 99 by multiplying all the matching prime factors to get a GCF of 33 and 99 as 1089:
Thus, the GCF of 33 and 99 is: 1089
How to Find the GCF of 33 and 99 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 33 and 99 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, 33 and 99:
Factors of 33: 1, 3, 11, 33
Factors of 99: 1, 3, 9, 11, 33, 99
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 33 and 99 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 30 and 102?
What is the GCF of 8 and 54?
What is the GCF of 131 and 138?
What is the GCF of 120 and 116?
What is the GCF of 38 and 141?