Solution: The GCF of 134 and 146 is 2
Methods
How to find the GCF of 134 and 146 using Prime Factorization
One way to find the GCF of 134 and 146 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 134?
What are the Factors of 146?
Here is the prime factorization of 134:
2
1
×
6
7
1
2^1 × 67^1
2 1 × 6 7 1
And this is the prime factorization of 146:
2
1
×
7
3
1
2^1 × 73^1
2 1 × 7 3 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 134 and 146 by multiplying all the matching prime factors to get a GCF of 134 and 146 as 4:
Thus, the GCF of 134 and 146 is: 4
How to Find the GCF of 134 and 146 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 134 and 146 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, 134 and 146:
Factors of 134: 1, 2, 67, 134
Factors of 146: 1, 2, 73, 146
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 134 and 146 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 32 and 84?
What is the GCF of 101 and 120?
What is the GCF of 100 and 85?
What is the GCF of 98 and 148?
What is the GCF of 142 and 30?