Solution: The GCF of 85 and 105 is 5
Methods
How to find the GCF of 85 and 105 using Prime Factorization
One way to find the GCF of 85 and 105 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 105?
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 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 1 × 5 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 105 by multiplying all the matching prime factors to get a GCF of 85 and 105 as 25:
Thus, the GCF of 85 and 105 is: 25
How to Find the GCF of 85 and 105 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 85 and 105 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 105:
Factors of 85: 1, 5, 17, 85
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
When you compare the two lists of factors, you can see that the common factor(s) are 1, 5. Since 5 is the largest of these common factors, the GCF of 85 and 105 would be 5.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 5 and 13?
What is the GCF of 82 and 12?
What is the GCF of 62 and 33?
What is the GCF of 90 and 116?
What is the GCF of 122 and 23?