Solution: The GCF of 124 and 116 is 4
Methods
How to find the GCF of 124 and 116 using Prime Factorization
One way to find the GCF of 124 and 116 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 124?
What are the Factors of 116?
Here is the prime factorization of 124:
2
2
×
3
1
1
2^2 × 31^1
2 2 × 3 1 1
And this is the prime factorization of 116:
2
2
×
2
9
1
2^2 × 29^1
2 2 × 2 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 124 and 116 by multiplying all the matching prime factors to get a GCF of 124 and 116 as 4:
Thus, the GCF of 124 and 116 is: 4
How to Find the GCF of 124 and 116 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 124 and 116 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, 124 and 116:
Factors of 124: 1, 2, 4, 31, 62, 124
Factors of 116: 1, 2, 4, 29, 58, 116
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4. Since 4 is the largest of these common factors, the GCF of 124 and 116 would be 4.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 136 and 149?
What is the GCF of 49 and 18?
What is the GCF of 125 and 89?
What is the GCF of 106 and 82?
What is the GCF of 102 and 108?