Solution: The GCF of 46 and 92 is 46
Methods
How to find the GCF of 46 and 92 using Prime Factorization
One way to find the GCF of 46 and 92 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 92?
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 92:
2
2
×
2
3
1
2^2 × 23^1
2 2 × 2 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 46 and 92 by multiplying all the matching prime factors to get a GCF of 46 and 92 as 2116:
Thus, the GCF of 46 and 92 is: 2116
How to Find the GCF of 46 and 92 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 46 and 92 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 92:
Factors of 46: 1, 2, 23, 46
Factors of 92: 1, 2, 4, 23, 46, 92
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 23, 46. Since 46 is the largest of these common factors, the GCF of 46 and 92 would be 46.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 16 and 20?
What is the GCF of 59 and 132?
What is the GCF of 22 and 6?
What is the GCF of 142 and 134?
What is the GCF of 89 and 58?