Solution: The GCF of 109 and 46 is 1
Methods
How to find the GCF of 109 and 46 using Prime Factorization
One way to find the GCF of 109 and 46 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 46?
Here is the prime factorization of 109:
10
9
1
109^1
10 9 1
And this is the prime factorization of 46:
2
1
×
2
3
1
2^1 × 23^1
2 1 × 2 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 109 and 46 is 1.
Thus, the GCF of 109 and 46 is: 1
How to Find the GCF of 109 and 46 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 109 and 46 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 46:
Factors of 109: 1, 109
Factors of 46: 1, 2, 23, 46
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 46 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 96 and 23?
What is the GCF of 50 and 68?
What is the GCF of 34 and 103?
What is the GCF of 100 and 76?
What is the GCF of 31 and 45?