Solution: The GCF of 119 and 34 is 17
Methods
How to find the GCF of 119 and 34 using Prime Factorization
One way to find the GCF of 119 and 34 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 119?
What are the Factors of 34?
Here is the prime factorization of 119:
7
1
×
1
7
1
7^1 × 17^1
7 1 × 1 7 1
And this is the prime factorization of 34:
2
1
×
1
7
1
2^1 × 17^1
2 1 × 1 7 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 119 and 34 by multiplying all the matching prime factors to get a GCF of 119 and 34 as 289:
Thus, the GCF of 119 and 34 is: 289
How to Find the GCF of 119 and 34 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 119 and 34 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, 119 and 34:
Factors of 119: 1, 7, 17, 119
Factors of 34: 1, 2, 17, 34
When you compare the two lists of factors, you can see that the common factor(s) are 1, 17. Since 17 is the largest of these common factors, the GCF of 119 and 34 would be 17.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 126 and 81?
What is the GCF of 141 and 86?
What is the GCF of 122 and 37?
What is the GCF of 129 and 34?
What is the GCF of 101 and 40?