Solution: The GCF of 82 and 135 is 1
Methods
How to find the GCF of 82 and 135 using Prime Factorization
One way to find the GCF of 82 and 135 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 82?
What are the Factors of 135?
Here is the prime factorization of 82:
2
1
×
4
1
1
2^1 × 41^1
2 1 × 4 1 1
And this is the prime factorization of 135:
3
3
×
5
1
3^3 × 5^1
3 3 × 5 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 82 and 135 is 1.
Thus, the GCF of 82 and 135 is: 1
How to Find the GCF of 82 and 135 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 82 and 135 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, 82 and 135:
Factors of 82: 1, 2, 41, 82
Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135
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 82 and 135 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 39 and 81?
What is the GCF of 104 and 31?
What is the GCF of 12 and 120?
What is the GCF of 129 and 106?
What is the GCF of 42 and 105?