Solution: The GCF of 44 and 6 is 2
Methods
How to find the GCF of 44 and 6 using Prime Factorization
One way to find the GCF of 44 and 6 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 44?
What are the Factors of 6?
Here is the prime factorization of 44:
2
2
×
1
1
1
2^2 × 11^1
2 2 × 1 1 1
And this is the prime factorization of 6:
2
1
×
3
1
2^1 × 3^1
2 1 × 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 44 and 6 by multiplying all the matching prime factors to get a GCF of 44 and 6 as 4:
Thus, the GCF of 44 and 6 is: 4
How to Find the GCF of 44 and 6 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 44 and 6 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, 44 and 6:
Factors of 44: 1, 2, 4, 11, 22, 44
Factors of 6: 1, 2, 3, 6
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 44 and 6 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 139 and 78?
What is the GCF of 92 and 143?
What is the GCF of 27 and 136?
What is the GCF of 5 and 134?
What is the GCF of 47 and 62?