Solution: The GCF of 83 and 78 is 1
Methods
How to find the GCF of 83 and 78 using Prime Factorization
One way to find the GCF of 83 and 78 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 83?
What are the Factors of 78?
Here is the prime factorization of 83:
8
3
1
83^1
8 3 1
And this 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
When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 83 and 78 is 1.
Thus, the GCF of 83 and 78 is: 1
How to Find the GCF of 83 and 78 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 83 and 78 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, 83 and 78:
Factors of 83: 1, 83
Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 83 and 78 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 123 and 70?
What is the GCF of 130 and 20?
What is the GCF of 59 and 1?
What is the GCF of 100 and 75?
What is the GCF of 12 and 51?