Solution: The GCF of 46 and 148 is 2
Methods
How to find the GCF of 46 and 148 using Prime Factorization
One way to find the GCF of 46 and 148 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 46?
What are the Factors of 148?
Here is the prime factorization of 46:
2
1
×
2
3
1
2^1 × 23^1
2 1 × 2 3 1
And this is the prime factorization of 148:
2
2
×
3
7
1
2^2 × 37^1
2 2 × 3 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 46 and 148 by multiplying all the matching prime factors to get a GCF of 46 and 148 as 4:
Thus, the GCF of 46 and 148 is: 4
How to Find the GCF of 46 and 148 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 46 and 148 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, 46 and 148:
Factors of 46: 1, 2, 23, 46
Factors of 148: 1, 2, 4, 37, 74, 148
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 46 and 148 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 48 and 13?
What is the GCF of 20 and 142?
What is the GCF of 123 and 119?
What is the GCF of 74 and 122?
What is the GCF of 7 and 121?