Solution: The GCF of 78 and 87 is 3
Methods
How to find the GCF of 78 and 87 using Prime Factorization
One way to find the GCF of 78 and 87 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 87?
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 87:
3
1
×
2
9
1
3^1 × 29^1
3 1 × 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 78 and 87 by multiplying all the matching prime factors to get a GCF of 78 and 87 as 9:
Thus, the GCF of 78 and 87 is: 9
How to Find the GCF of 78 and 87 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 78 and 87 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 87:
Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
Factors of 87: 1, 3, 29, 87
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3. Since 3 is the largest of these common factors, the GCF of 78 and 87 would be 3.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 47 and 89?
What is the GCF of 17 and 49?
What is the GCF of 33 and 112?
What is the GCF of 69 and 135?
What is the GCF of 44 and 86?