Solution: The GCF of 108 and 82 is 2
Methods
How to find the GCF of 108 and 82 using Prime Factorization
One way to find the GCF of 108 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 108?
What are the Factors of 82?
Here is the prime factorization of 108:
2
2
×
3
3
2^2 × 3^3
2 2 × 3 3
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 matching prime factors. You can now find the Greatest Common Factor of 108 and 82 by multiplying all the matching prime factors to get a GCF of 108 and 82 as 4:
Thus, the GCF of 108 and 82 is: 4
How to Find the GCF of 108 and 82 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 108 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, 108 and 82:
Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 82: 1, 2, 41, 82
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 108 and 82 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 142 and 85?
What is the GCF of 27 and 80?
What is the GCF of 62 and 3?
What is the GCF of 43 and 82?
What is the GCF of 105 and 49?