Solution: The GCF of 30 and 122 is 2
Methods
How to find the GCF of 30 and 122 using Prime Factorization
One way to find the GCF of 30 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 30?
What are the Factors of 122?
Here is the prime factorization of 30:
2
1
×
3
1
×
5
1
2^1 × 3^1 × 5^1
2 1 × 3 1 × 5 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 matching prime factors. You can now find the Greatest Common Factor of 30 and 122 by multiplying all the matching prime factors to get a GCF of 30 and 122 as 4:
Thus, the GCF of 30 and 122 is: 4
How to Find the GCF of 30 and 122 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 30 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, 30 and 122:
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 122: 1, 2, 61, 122
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 30 and 122 would be 2.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 102 and 23?
What is the GCF of 22 and 145?
What is the GCF of 39 and 51?
What is the GCF of 144 and 56?
What is the GCF of 100 and 121?