Solution: The GCF of 120 and 42 is 6
Methods
How to find the GCF of 120 and 42 using Prime Factorization
One way to find the GCF of 120 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 120?
What are the Factors of 42?
Here is the prime factorization of 120:
2
3
×
3
1
×
5
1
2^3 × 3^1 × 5^1
2 3 × 3 1 × 5 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 120 and 42 by multiplying all the matching prime factors to get a GCF of 120 and 42 as 36:
Thus, the GCF of 120 and 42 is: 36
How to Find the GCF of 120 and 42 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 120 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, 120 and 42:
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
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, 3, 6. Since 6 is the largest of these common factors, the GCF of 120 and 42 would be 6.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 41 and 38?
What is the GCF of 86 and 29?
What is the GCF of 100 and 95?
What is the GCF of 106 and 15?
What is the GCF of 102 and 61?