Solution: The GCF of 19 and 118 is 1
Methods
How to find the GCF of 19 and 118 using Prime Factorization
One way to find the GCF of 19 and 118 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 19?
What are the Factors of 118?
Here is the prime factorization of 19:
1
9
1
19^1
1 9 1
And this is the prime factorization of 118:
2
1
×
5
9
1
2^1 × 59^1
2 1 × 5 9 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 19 and 118 is 1.
Thus, the GCF of 19 and 118 is: 1
How to Find the GCF of 19 and 118 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 19 and 118 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, 19 and 118:
Factors of 19: 1, 19
Factors of 118: 1, 2, 59, 118
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 19 and 118 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 2 and 31?
What is the GCF of 15 and 120?
What is the GCF of 103 and 149?
What is the GCF of 105 and 63?
What is the GCF of 42 and 128?