Solution: The GCF of 36 and 34 is 2
Methods
How to find the GCF of 36 and 34 using Prime Factorization
One way to find the GCF of 36 and 34 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 36?
What are the Factors of 34?
Here is the prime factorization of 36:
2
2
×
3
2
2^2 × 3^2
2 2 × 3 2
And this is the prime factorization of 34:
2
1
×
1
7
1
2^1 × 17^1
2 1 × 1 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 36 and 34 by multiplying all the matching prime factors to get a GCF of 36 and 34 as 4:
Thus, the GCF of 36 and 34 is: 4
How to Find the GCF of 36 and 34 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 36 and 34 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, 36 and 34:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 34: 1, 2, 17, 34
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 36 and 34 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 69 and 37?
What is the GCF of 71 and 50?
What is the GCF of 109 and 53?
What is the GCF of 83 and 30?
What is the GCF of 49 and 113?