Solution: The GCF of 150 and 75 is 75
Methods
How to find the GCF of 150 and 75 using Prime Factorization
One way to find the GCF of 150 and 75 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 75?
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 75:
3
1
×
5
2
3^1 × 5^2
3 1 × 5 2
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 75 by multiplying all the matching prime factors to get a GCF of 150 and 75 as 225:
Thus, the GCF of 150 and 75 is: 225
How to Find the GCF of 150 and 75 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 150 and 75 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 75:
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 75: 1, 3, 5, 15, 25, 75
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 5, 15, 25, 75. Since 75 is the largest of these common factors, the GCF of 150 and 75 would be 75.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 27 and 106?
What is the GCF of 55 and 45?
What is the GCF of 123 and 77?
What is the GCF of 80 and 112?
What is the GCF of 40 and 127?