MATH SOLVE

1 month ago

Q:
# What is the GCF of 16 and 128?

Accepted Solution

A:

Solution: The GCF of 16 and 128 is 16
Methods
How to find the GCF of 16 and 128 using Prime Factorization
One way to find the GCF of 16 and 128 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 16?
What are the Factors of 128?
Here is the prime factorization of 16:
2
4
2^4
2 4
And this is the prime factorization of 128:
2
7
2^7
2 7
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 16 and 128 by multiplying all the matching prime factors to get a GCF of 16 and 128 as 4:
Thus, the GCF of 16 and 128 is: 4
How to Find the GCF of 16 and 128 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 16 and 128 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, 16 and 128:
Factors of 16: 1, 2, 4, 8, 16
Factors of 128: 1, 2, 4, 8, 16, 32, 64, 128
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 8, 16. Since 16 is the largest of these common factors, the GCF of 16 and 128 would be 16.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 59 and 18?
What is the GCF of 147 and 105?
What is the GCF of 80 and 79?
What is the GCF of 111 and 52?
What is the GCF of 27 and 25?