MATH SOLVE

3 months ago

Q:
# What is the GCF of 36 and 82?

Accepted Solution

A:

Solution: The GCF of 36 and 82 is 2
Methods
How to find the GCF of 36 and 82 using Prime Factorization
One way to find the GCF of 36 and 82 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 82?
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 82:
2
1
×
4
1
1
2^1 × 41^1
2 1 × 4 1 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 82 by multiplying all the matching prime factors to get a GCF of 36 and 82 as 4:
Thus, the GCF of 36 and 82 is: 4
How to Find the GCF of 36 and 82 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 36 and 82 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 82:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 82: 1, 2, 41, 82
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 36 and 82 would be 2.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 114 and 56?
What is the GCF of 71 and 84?
What is the GCF of 108 and 23?
What is the GCF of 35 and 44?
What is the GCF of 109 and 79?