Solution: The GCF of 100 and 75 is 25
Methods
How to find the GCF of 100 and 75 using Prime Factorization
One way to find the GCF of 100 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 100?
What are the Factors of 75?
Here is the prime factorization of 100:
2
2
×
5
2
2^2 × 5^2
2 2 × 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 100 and 75 by multiplying all the matching prime factors to get a GCF of 100 and 75 as 25:
Thus, the GCF of 100 and 75 is: 25
How to Find the GCF of 100 and 75 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 100 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, 100 and 75:
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
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, 5, 25. Since 25 is the largest of these common factors, the GCF of 100 and 75 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 12 and 123?
What is the GCF of 15 and 126?
What is the GCF of 104 and 66?
What is the GCF of 13 and 144?
What is the GCF of 63 and 20?