Solution: The GCF of 3 and 6 is 3
Methods
How to find the GCF of 3 and 6 using Prime Factorization
One way to find the GCF of 3 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 3?
What are the Factors of 6?
Here is the prime factorization of 3:
3
1
3^1
3 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 3 and 6 by multiplying all the matching prime factors to get a GCF of 3 and 6 as 9:
Thus, the GCF of 3 and 6 is: 9
How to Find the GCF of 3 and 6 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 3 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, 3 and 6:
Factors of 3: 1, 3
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, 3. Since 3 is the largest of these common factors, the GCF of 3 and 6 would be 3.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 40 and 14?
What is the GCF of 29 and 53?
What is the GCF of 36 and 1?
What is the GCF of 121 and 105?
What is the GCF of 52 and 136?