Solution: The GCF of 84 and 112 is 28
Methods
How to find the GCF of 84 and 112 using Prime Factorization
One way to find the GCF of 84 and 112 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 84?
What are the Factors of 112?
Here is the prime factorization of 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 1 × 7 1
And this is the prime factorization of 112:
2
4
×
7
1
2^4 × 7^1
2 4 × 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 84 and 112 by multiplying all the matching prime factors to get a GCF of 84 and 112 as 196:
Thus, the GCF of 84 and 112 is: 196
How to Find the GCF of 84 and 112 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 84 and 112 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, 84 and 112:
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 7, 14, 28. Since 28 is the largest of these common factors, the GCF of 84 and 112 would be 28.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 61 and 100?
What is the GCF of 146 and 150?
What is the GCF of 8 and 116?
What is the GCF of 55 and 21?
What is the GCF of 4 and 115?