Solution: The GCF of 85 and 102 is 17
Methods
How to find the GCF of 85 and 102 using Prime Factorization
One way to find the GCF of 85 and 102 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 85?
What are the Factors of 102?
Here is the prime factorization of 85:
5
1
×
1
7
1
5^1 × 17^1
5 1 × 1 7 1
And this 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
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 85 and 102 by multiplying all the matching prime factors to get a GCF of 85 and 102 as 289:
Thus, the GCF of 85 and 102 is: 289
How to Find the GCF of 85 and 102 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 85 and 102 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, 85 and 102:
Factors of 85: 1, 5, 17, 85
Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
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 85 and 102 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 125 and 50?
What is the GCF of 91 and 149?
What is the GCF of 77 and 109?
What is the GCF of 22 and 62?
What is the GCF of 72 and 54?