Solution: The GCF of 114 and 19 is 19
Methods
How to find the GCF of 114 and 19 using Prime Factorization
One way to find the GCF of 114 and 19 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 114?
What are the Factors of 19?
Here is the prime factorization of 114:
2
1
×
3
1
×
1
9
1
2^1 × 3^1 × 19^1
2 1 × 3 1 × 1 9 1
And this is the prime factorization of 19:
1
9
1
19^1
1 9 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 114 and 19 by multiplying all the matching prime factors to get a GCF of 114 and 19 as 361:
Thus, the GCF of 114 and 19 is: 361
How to Find the GCF of 114 and 19 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 114 and 19 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, 114 and 19:
Factors of 114: 1, 2, 3, 6, 19, 38, 57, 114
Factors of 19: 1, 19
When you compare the two lists of factors, you can see that the common factor(s) are 1, 19. Since 19 is the largest of these common factors, the GCF of 114 and 19 would be 19.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 48 and 105?
What is the GCF of 120 and 90?
What is the GCF of 30 and 22?
What is the GCF of 88 and 69?
What is the GCF of 77 and 1?