Solution: The GCF of 102 and 51 is 51
Methods
How to find the GCF of 102 and 51 using Prime Factorization
One way to find the GCF of 102 and 51 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 102?
What are the Factors of 51?
Here is the prime factorization of 102:
2
1
×
3
1
×
1
7
1
2^1 × 3^1 × 17^1
2 1 × 3 1 × 1 7 1
And this is the prime factorization of 51:
3
1
×
1
7
1
3^1 × 17^1
3 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 102 and 51 by multiplying all the matching prime factors to get a GCF of 102 and 51 as 2601:
Thus, the GCF of 102 and 51 is: 2601
How to Find the GCF of 102 and 51 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 102 and 51 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, 102 and 51:
Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
Factors of 51: 1, 3, 17, 51
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 17, 51. Since 51 is the largest of these common factors, the GCF of 102 and 51 would be 51.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 17 and 123?
What is the GCF of 71 and 143?
What is the GCF of 54 and 58?
What is the GCF of 22 and 132?
What is the GCF of 7 and 128?