Solution: The GCF of 75 and 5 is 5
Methods
How to find the GCF of 75 and 5 using Prime Factorization
One way to find the GCF of 75 and 5 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 5?
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 5:
5
1
5^1
5 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 75 and 5 by multiplying all the matching prime factors to get a GCF of 75 and 5 as 25:
Thus, the GCF of 75 and 5 is: 25
How to Find the GCF of 75 and 5 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 75 and 5 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 5:
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 5: 1, 5
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 75 and 5 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 150 and 100?
What is the GCF of 108 and 30?
What is the GCF of 89 and 6?
What is the GCF of 53 and 10?
What is the GCF of 111 and 82?