MATH SOLVE

3 months ago

Q:
# What is the GCF of 74 and 16?

Accepted Solution

A:

Solution: The GCF of 74 and 16 is 2
Methods
How to find the GCF of 74 and 16 using Prime Factorization
One way to find the GCF of 74 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 74?
What are the Factors of 16?
Here is the prime factorization of 74:
2
1
×
3
7
1
2^1 × 37^1
2 1 × 3 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 74 and 16 by multiplying all the matching prime factors to get a GCF of 74 and 16 as 4:
Thus, the GCF of 74 and 16 is: 4
How to Find the GCF of 74 and 16 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 74 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, 74 and 16:
Factors of 74: 1, 2, 37, 74
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 74 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 115 and 51?
What is the GCF of 110 and 118?
What is the GCF of 124 and 8?
What is the GCF of 141 and 61?
What is the GCF of 21 and 108?