Solution: The GCF of 150 and 125 is 25
Methods
How to find the GCF of 150 and 125 using Prime Factorization
One way to find the GCF of 150 and 125 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 150?
What are the Factors of 125?
Here is the prime factorization of 150:
2
1
×
3
1
×
5
2
2^1 × 3^1 × 5^2
2 1 × 3 1 × 5 2
And this is the prime factorization of 125:
5
3
5^3
5 3
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 150 and 125 by multiplying all the matching prime factors to get a GCF of 150 and 125 as 25:
Thus, the GCF of 150 and 125 is: 25
How to Find the GCF of 150 and 125 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 150 and 125 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, 150 and 125:
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 125: 1, 5, 25, 125
When you compare the two lists of factors, you can see that the common factor(s) are 1, 5, 25. Since 25 is the largest of these common factors, the GCF of 150 and 125 would be 25.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 68 and 14?
What is the GCF of 33 and 36?
What is the GCF of 69 and 38?
What is the GCF of 77 and 25?
What is the GCF of 101 and 59?