Solution: The GCF of 118 and 52 is 2
Methods
How to find the GCF of 118 and 52 using Prime Factorization
One way to find the GCF of 118 and 52 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 118?
What are the Factors of 52?
Here is the prime factorization of 118:
2
1
×
5
9
1
2^1 × 59^1
2 1 × 5 9 1
And this is the prime factorization of 52:
2
2
×
1
3
1
2^2 × 13^1
2 2 × 1 3 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 118 and 52 by multiplying all the matching prime factors to get a GCF of 118 and 52 as 4:
Thus, the GCF of 118 and 52 is: 4
How to Find the GCF of 118 and 52 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 118 and 52 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, 118 and 52:
Factors of 118: 1, 2, 59, 118
Factors of 52: 1, 2, 4, 13, 26, 52
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 118 and 52 would be 2.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 145 and 142?
What is the GCF of 109 and 96?
What is the GCF of 130 and 125?
What is the GCF of 140 and 91?
What is the GCF of 51 and 56?