Solution: The GCF of 19 and 57 is 19
Methods
How to find the GCF of 19 and 57 using Prime Factorization
One way to find the GCF of 19 and 57 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 57?
Here is the prime factorization of 19:
1
9
1
19^1
1 9 1
And this is the prime factorization of 57:
3
1
×
1
9
1
3^1 × 19^1
3 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 19 and 57 by multiplying all the matching prime factors to get a GCF of 19 and 57 as 361:
Thus, the GCF of 19 and 57 is: 361
How to Find the GCF of 19 and 57 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 19 and 57 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 57:
Factors of 19: 1, 19
Factors of 57: 1, 3, 19, 57
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 19 and 57 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 7 and 137?
What is the GCF of 60 and 40?
What is the GCF of 35 and 69?
What is the GCF of 58 and 92?
What is the GCF of 112 and 61?