Solution: The GCF of 125 and 35 is 5
Methods
How to find the GCF of 125 and 35 using Prime Factorization
One way to find the GCF of 125 and 35 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 125?
What are the Factors of 35?
Here is the prime factorization of 125:
5
3
5^3
5 3
And this is the prime factorization of 35:
5
1
×
7
1
5^1 × 7^1
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 125 and 35 by multiplying all the matching prime factors to get a GCF of 125 and 35 as 25:
Thus, the GCF of 125 and 35 is: 25
How to Find the GCF of 125 and 35 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 125 and 35 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, 125 and 35:
Factors of 125: 1, 5, 25, 125
Factors of 35: 1, 5, 7, 35
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 125 and 35 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 14 and 149?
What is the GCF of 45 and 116?
What is the GCF of 59 and 82?
What is the GCF of 67 and 111?
What is the GCF of 137 and 139?