MATH SOLVE

4 months ago

Q:
# What is the GCF of 74 and 84?

Accepted Solution

A:

Solution: The GCF of 74 and 84 is 2
Methods
How to find the GCF of 74 and 84 using Prime Factorization
One way to find the GCF of 74 and 84 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 84?
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 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 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 74 and 84 by multiplying all the matching prime factors to get a GCF of 74 and 84 as 4:
Thus, the GCF of 74 and 84 is: 4
How to Find the GCF of 74 and 84 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 74 and 84 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 84:
Factors of 74: 1, 2, 37, 74
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
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 84 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 141 and 37?
What is the GCF of 120 and 29?
What is the GCF of 6 and 97?
What is the GCF of 110 and 149?
What is the GCF of 94 and 134?