Solution: The GCF of 34 and 85 is 17
Methods
How to find the GCF of 34 and 85 using Prime Factorization
One way to find the GCF of 34 and 85 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 34?
What are the Factors of 85?
Here is the prime factorization of 34:
2
1
×
1
7
1
2^1 × 17^1
2 1 × 1 7 1
And this is the prime factorization of 85:
5
1
×
1
7
1
5^1 × 17^1
5 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 34 and 85 by multiplying all the matching prime factors to get a GCF of 34 and 85 as 289:
Thus, the GCF of 34 and 85 is: 289
How to Find the GCF of 34 and 85 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 34 and 85 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, 34 and 85:
Factors of 34: 1, 2, 17, 34
Factors of 85: 1, 5, 17, 85
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 34 and 85 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 131 and 21?
What is the GCF of 73 and 101?
What is the GCF of 35 and 5?
What is the GCF of 135 and 137?
What is the GCF of 88 and 108?