Solution: The GCF of 19 and 95 is 19
Methods
How to find the GCF of 19 and 95 using Prime Factorization
One way to find the GCF of 19 and 95 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 95?
Here is the prime factorization of 19:
1
9
1
19^1
1 9 1
And this is the prime factorization of 95:
5
1
×
1
9
1
5^1 × 19^1
5 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 95 by multiplying all the matching prime factors to get a GCF of 19 and 95 as 361:
Thus, the GCF of 19 and 95 is: 361
How to Find the GCF of 19 and 95 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 19 and 95 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 95:
Factors of 19: 1, 19
Factors of 95: 1, 5, 19, 95
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 95 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 99 and 98?
What is the GCF of 22 and 58?
What is the GCF of 141 and 117?
What is the GCF of 11 and 113?
What is the GCF of 45 and 6?