MATH SOLVE

4 months ago

Q:
# What is the GCF of 72 and 57?

Accepted Solution

A:

Solution: The GCF of 72 and 57 is 3
Methods
How to find the GCF of 72 and 57 using Prime Factorization
One way to find the GCF of 72 and 57 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 72?
What are the Factors of 57?
Here is the prime factorization of 72:
2
3
×
3
2
2^3 × 3^2
2 3 × 3 2
And this is the prime factorization of 57:
3
1
×
1
9
1
3^1 × 19^1
3 1 × 1 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 72 and 57 by multiplying all the matching prime factors to get a GCF of 72 and 57 as 9:
Thus, the GCF of 72 and 57 is: 9
How to Find the GCF of 72 and 57 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 72 and 57 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, 72 and 57:
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 57: 1, 3, 19, 57
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 72 and 57 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 122 and 53?
What is the GCF of 118 and 81?
What is the GCF of 7 and 144?
What is the GCF of 2 and 112?
What is the GCF of 108 and 90?