Solution: The GCF of 112 and 42 is 14
Methods
How to find the GCF of 112 and 42 using Prime Factorization
One way to find the GCF of 112 and 42 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 112?
What are the Factors of 42?
Here is the prime factorization of 112:
2
4
×
7
1
2^4 × 7^1
2 4 × 7 1
And this is the prime factorization of 42:
2
1
×
3
1
×
7
1
2^1 × 3^1 × 7^1
2 1 × 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 112 and 42 by multiplying all the matching prime factors to get a GCF of 112 and 42 as 196:
Thus, the GCF of 112 and 42 is: 196
How to Find the GCF of 112 and 42 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 112 and 42 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, 112 and 42:
Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 7, 14. Since 14 is the largest of these common factors, the GCF of 112 and 42 would be 14.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 4 and 46?
What is the GCF of 14 and 12?
What is the GCF of 122 and 16?
What is the GCF of 104 and 121?
What is the GCF of 139 and 108?