Solution: The GCF of 102 and 119 is 17
Methods
How to find the GCF of 102 and 119 using Prime Factorization
One way to find the GCF of 102 and 119 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 102?
What are the Factors of 119?
Here is the prime factorization of 102:
2
1
×
3
1
×
1
7
1
2^1 × 3^1 × 17^1
2 1 × 3 1 × 1 7 1
And this is the prime factorization of 119:
7
1
×
1
7
1
7^1 × 17^1
7 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 102 and 119 by multiplying all the matching prime factors to get a GCF of 102 and 119 as 289:
Thus, the GCF of 102 and 119 is: 289
How to Find the GCF of 102 and 119 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 102 and 119 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, 102 and 119:
Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
Factors of 119: 1, 7, 17, 119
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 102 and 119 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 113 and 140?
What is the GCF of 28 and 42?
What is the GCF of 79 and 90?
What is the GCF of 121 and 40?
What is the GCF of 124 and 26?