Solution: The GCF of 78 and 118 is 2
Methods
How to find the GCF of 78 and 118 using Prime Factorization
One way to find the GCF of 78 and 118 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 78?
What are the Factors of 118?
Here is the prime factorization of 78:
2
1
×
3
1
×
1
3
1
2^1 × 3^1 × 13^1
2 1 × 3 1 × 1 3 1
And this is the prime factorization of 118:
2
1
×
5
9
1
2^1 × 59^1
2 1 × 5 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 78 and 118 by multiplying all the matching prime factors to get a GCF of 78 and 118 as 4:
Thus, the GCF of 78 and 118 is: 4
How to Find the GCF of 78 and 118 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 78 and 118 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, 78 and 118:
Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
Factors of 118: 1, 2, 59, 118
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 78 and 118 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 6 and 22?
What is the GCF of 128 and 29?
What is the GCF of 97 and 127?
What is the GCF of 106 and 3?
What is the GCF of 77 and 90?