Solution: The GCF of 117 and 33 is 3
Methods
How to find the GCF of 117 and 33 using Prime Factorization
One way to find the GCF of 117 and 33 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 117?
What are the Factors of 33?
Here is the prime factorization of 117:
3
2
×
1
3
1
3^2 × 13^1
3 2 × 1 3 1
And this is the prime factorization of 33:
3
1
×
1
1
1
3^1 × 11^1
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 117 and 33 by multiplying all the matching prime factors to get a GCF of 117 and 33 as 9:
Thus, the GCF of 117 and 33 is: 9
How to Find the GCF of 117 and 33 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 117 and 33 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, 117 and 33:
Factors of 117: 1, 3, 9, 13, 39, 117
Factors of 33: 1, 3, 11, 33
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3. Since 3 is the largest of these common factors, the GCF of 117 and 33 would be 3.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 15 and 2?
What is the GCF of 61 and 6?
What is the GCF of 59 and 109?
What is the GCF of 143 and 139?
What is the GCF of 65 and 63?