Solution: The GCF of 35 and 82 is 1
Methods
How to find the GCF of 35 and 82 using Prime Factorization
One way to find the GCF of 35 and 82 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 35?
What are the Factors of 82?
Here is the prime factorization of 35:
5
1
×
7
1
5^1 × 7^1
5 1 × 7 1
And this is the prime factorization of 82:
2
1
×
4
1
1
2^1 × 41^1
2 1 × 4 1 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 35 and 82 is 1.
Thus, the GCF of 35 and 82 is: 1
How to Find the GCF of 35 and 82 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 35 and 82 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, 35 and 82:
Factors of 35: 1, 5, 7, 35
Factors of 82: 1, 2, 41, 82
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 35 and 82 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 37 and 79?
What is the GCF of 84 and 47?
What is the GCF of 45 and 141?
What is the GCF of 71 and 82?
What is the GCF of 73 and 78?