Solution: The GCF of 75 and 145 is 5
Methods
How to find the GCF of 75 and 145 using Prime Factorization
One way to find the GCF of 75 and 145 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 145?
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 145:
5
1
×
2
9
1
5^1 × 29^1
5 1 × 2 9 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 145 by multiplying all the matching prime factors to get a GCF of 75 and 145 as 25:
Thus, the GCF of 75 and 145 is: 25
How to Find the GCF of 75 and 145 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 75 and 145 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 145:
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 145: 1, 5, 29, 145
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 145 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 116 and 149?
What is the GCF of 48 and 106?
What is the GCF of 84 and 96?
What is the GCF of 54 and 34?
What is the GCF of 114 and 128?