Solution: The GCF of 109 and 84 is 1
Methods
How to find the GCF of 109 and 84 using Prime Factorization
One way to find the GCF of 109 and 84 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 109?
What are the Factors of 84?
Here is the prime factorization of 109:
10
9
1
109^1
10 9 1
And this is the prime factorization of 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 1 × 7 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 109 and 84 is 1.
Thus, the GCF of 109 and 84 is: 1
How to Find the GCF of 109 and 84 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 109 and 84 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, 109 and 84:
Factors of 109: 1, 109
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
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 109 and 84 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 21 and 98?
What is the GCF of 94 and 24?
What is the GCF of 41 and 39?
What is the GCF of 89 and 56?
What is the GCF of 138 and 128?