Solution: The GCF of 101 and 122 is 1
Methods
How to find the GCF of 101 and 122 using Prime Factorization
One way to find the GCF of 101 and 122 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 101?
What are the Factors of 122?
Here is the prime factorization of 101:
10
1
1
101^1
10 1 1
And this is the prime factorization of 122:
2
1
×
6
1
1
2^1 × 61^1
2 1 × 6 1 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 101 and 122 is 1.
Thus, the GCF of 101 and 122 is: 1
How to Find the GCF of 101 and 122 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 101 and 122 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, 101 and 122:
Factors of 101: 1, 101
Factors of 122: 1, 2, 61, 122
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 101 and 122 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 7 and 92?
What is the GCF of 111 and 11?
What is the GCF of 91 and 104?
What is the GCF of 105 and 143?
What is the GCF of 51 and 98?