MATH SOLVE

4 months ago

Q:
# What is the GCF of 68 and 27?

Accepted Solution

A:

Solution: The GCF of 68 and 27 is 1
Methods
How to find the GCF of 68 and 27 using Prime Factorization
One way to find the GCF of 68 and 27 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 68?
What are the Factors of 27?
Here is the prime factorization of 68:
2
2
×
1
7
1
2^2 × 17^1
2 2 × 1 7 1
And this is the prime factorization of 27:
3
3
3^3
3 3
When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 68 and 27 is 1.
Thus, the GCF of 68 and 27 is: 1
How to Find the GCF of 68 and 27 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 68 and 27 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, 68 and 27:
Factors of 68: 1, 2, 4, 17, 34, 68
Factors of 27: 1, 3, 9, 27
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 68 and 27 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 90 and 110?
What is the GCF of 89 and 86?
What is the GCF of 58 and 36?
What is the GCF of 75 and 82?
What is the GCF of 31 and 23?