Solution: The GCF of 102 and 16 is 2
Methods
How to find the GCF of 102 and 16 using Prime Factorization
One way to find the GCF of 102 and 16 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 16?
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 16:
2
4
2^4
2 4
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 16 by multiplying all the matching prime factors to get a GCF of 102 and 16 as 4:
Thus, the GCF of 102 and 16 is: 4
How to Find the GCF of 102 and 16 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 102 and 16 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 16:
Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
Factors of 16: 1, 2, 4, 8, 16
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 102 and 16 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 96 and 131?
What is the GCF of 30 and 51?
What is the GCF of 121 and 137?
What is the GCF of 40 and 5?
What is the GCF of 81 and 136?