MATH SOLVE

4 months ago

Q:
# What is the GCF of 21 and 120?

Accepted Solution

A:

Solution: The GCF of 21 and 120 is 3
Methods
How to find the GCF of 21 and 120 using Prime Factorization
One way to find the GCF of 21 and 120 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 120?
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 120:
2
3
×
3
1
×
5
1
2^3 × 3^1 × 5^1
2 3 × 3 1 × 5 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 21 and 120 by multiplying all the matching prime factors to get a GCF of 21 and 120 as 9:
Thus, the GCF of 21 and 120 is: 9
How to Find the GCF of 21 and 120 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 21 and 120 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 120:
Factors of 21: 1, 3, 7, 21
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
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 21 and 120 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 94 and 69?
What is the GCF of 121 and 93?
What is the GCF of 38 and 72?
What is the GCF of 20 and 66?
What is the GCF of 129 and 60?