Solution: The GCF of 36 and 114 is 6
Methods
How to find the GCF of 36 and 114 using Prime Factorization
One way to find the GCF of 36 and 114 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 36?
What are the Factors of 114?
Here is the prime factorization of 36:
2
2
×
3
2
2^2 × 3^2
2 2 × 3 2
And this is the prime factorization of 114:
2
1
×
3
1
×
1
9
1
2^1 × 3^1 × 19^1
2 1 × 3 1 × 1 9 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 36 and 114 by multiplying all the matching prime factors to get a GCF of 36 and 114 as 36:
Thus, the GCF of 36 and 114 is: 36
How to Find the GCF of 36 and 114 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 36 and 114 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, 36 and 114:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 114: 1, 2, 3, 6, 19, 38, 57, 114
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6. Since 6 is the largest of these common factors, the GCF of 36 and 114 would be 6.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 78 and 101?
What is the GCF of 62 and 105?
What is the GCF of 26 and 122?
What is the GCF of 59 and 89?
What is the GCF of 17 and 133?