MATH SOLVE

1 month ago

Q:
# What is the GCF of 21 and 68?

Accepted Solution

A:

Solution: The GCF of 21 and 68 is 1
Methods
How to find the GCF of 21 and 68 using Prime Factorization
One way to find the GCF of 21 and 68 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 21?
What are the Factors of 68?
Here is the prime factorization of 21:
3
1
×
7
1
3^1 × 7^1
3 1 × 7 1
And this is the prime factorization of 68:
2
2
×
1
7
1
2^2 × 17^1
2 2 × 1 7 1
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 21 and 68 is 1.
Thus, the GCF of 21 and 68 is: 1
How to Find the GCF of 21 and 68 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 21 and 68 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, 21 and 68:
Factors of 21: 1, 3, 7, 21
Factors of 68: 1, 2, 4, 17, 34, 68
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 21 and 68 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 43 and 82?
What is the GCF of 23 and 10?
What is the GCF of 68 and 102?
What is the GCF of 67 and 42?
What is the GCF of 33 and 7?