MATH SOLVE

1 month ago

Q:
# What is the GCF of 36 and 84?

Accepted Solution

A:

Solution: The GCF of 36 and 84 is 12
Methods
How to find the GCF of 36 and 84 using Prime Factorization
One way to find the GCF of 36 and 84 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 36?
What are the Factors of 84?
Here is the prime factorization of 36:
2
2
×
3
2
2^2 × 3^2
2 2 × 3 2
And this is the prime factorization of 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 1 × 7 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 36 and 84 by multiplying all the matching prime factors to get a GCF of 36 and 84 as 36:
Thus, the GCF of 36 and 84 is: 36
How to Find the GCF of 36 and 84 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 36 and 84 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, 36 and 84:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 4, 6, 12. Since 12 is the largest of these common factors, the GCF of 36 and 84 would be 12.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 30 and 122?
What is the GCF of 49 and 145?
What is the GCF of 82 and 40?
What is the GCF of 70 and 138?
What is the GCF of 116 and 62?