Solution: The GCF of 76 and 114 is 38
Methods
How to find the GCF of 76 and 114 using Prime Factorization
One way to find the GCF of 76 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 76?
What are the Factors of 114?
Here is the prime factorization of 76:
2
2
×
1
9
1
2^2 × 19^1
2 2 × 1 9 1
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 76 and 114 by multiplying all the matching prime factors to get a GCF of 76 and 114 as 1444:
Thus, the GCF of 76 and 114 is: 1444
How to Find the GCF of 76 and 114 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 76 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, 76 and 114:
Factors of 76: 1, 2, 4, 19, 38, 76
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, 19, 38. Since 38 is the largest of these common factors, the GCF of 76 and 114 would be 38.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 35 and 144?
What is the GCF of 146 and 15?
What is the GCF of 94 and 51?
What is the GCF of 16 and 44?
What is the GCF of 37 and 111?