Solution: The GCF of 75 and 50 is 25
Methods
How to find the GCF of 75 and 50 using Prime Factorization
One way to find the GCF of 75 and 50 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 75?
What are the Factors of 50?
Here is the prime factorization of 75:
3
1
×
5
2
3^1 × 5^2
3 1 × 5 2
And this is the prime factorization of 50:
2
1
×
5
2
2^1 × 5^2
2 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 75 and 50 by multiplying all the matching prime factors to get a GCF of 75 and 50 as 25:
Thus, the GCF of 75 and 50 is: 25
How to Find the GCF of 75 and 50 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 75 and 50 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, 75 and 50:
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 50: 1, 2, 5, 10, 25, 50
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 75 and 50 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 11 and 53?
What is the GCF of 71 and 17?
What is the GCF of 61 and 38?
What is the GCF of 45 and 130?
What is the GCF of 64 and 39?