Solution: The GCF of 71 and 120 is 1
Methods
How to find the GCF of 71 and 120 using Prime Factorization
One way to find the GCF of 71 and 120 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 71?
What are the Factors of 120?
Here is the prime factorization of 71:
7
1
1
71^1
7 1 1
And this is the prime factorization of 120:
2
3
×
3
1
×
5
1
2^3 × 3^1 × 5^1
2 3 × 3 1 × 5 1
When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 71 and 120 is 1.
Thus, the GCF of 71 and 120 is: 1
How to Find the GCF of 71 and 120 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 71 and 120 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, 71 and 120:
Factors of 71: 1, 71
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 71 and 120 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 41 and 18?
What is the GCF of 125 and 119?
What is the GCF of 115 and 8?
What is the GCF of 49 and 149?
What is the GCF of 78 and 111?