MATH SOLVE

3 months ago

Q:
# What is the GCF of 75 and 66?

Accepted Solution

A:

Solution: The GCF of 75 and 66 is 3
Methods
How to find the GCF of 75 and 66 using Prime Factorization
One way to find the GCF of 75 and 66 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 66?
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 66:
2
1
×
3
1
×
1
1
1
2^1 × 3^1 × 11^1
2 1 × 3 1 × 1 1 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 66 by multiplying all the matching prime factors to get a GCF of 75 and 66 as 9:
Thus, the GCF of 75 and 66 is: 9
How to Find the GCF of 75 and 66 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 75 and 66 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 66:
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3. Since 3 is the largest of these common factors, the GCF of 75 and 66 would be 3.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 21 and 17?
What is the GCF of 69 and 32?
What is the GCF of 60 and 142?
What is the GCF of 84 and 98?
What is the GCF of 150 and 83?