MATH SOLVE

3 months ago

Q:
# What is the GCF of 49 and 66?

Accepted Solution

A:

Solution: The GCF of 49 and 66 is 1
Methods
How to find the GCF of 49 and 66 using Prime Factorization
One way to find the GCF of 49 and 66 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 49?
What are the Factors of 66?
Here is the prime factorization of 49:
7
2
7^2
7 2
And this is the prime factorization of 66:
2
1
×
3
1
×
1
1
1
2^1 × 3^1 × 11^1
2 1 × 3 1 × 1 1 1
When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 49 and 66 is 1.
Thus, the GCF of 49 and 66 is: 1
How to Find the GCF of 49 and 66 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 49 and 66 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, 49 and 66:
Factors of 49: 1, 7, 49
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 49 and 66 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 35 and 57?
What is the GCF of 32 and 97?
What is the GCF of 73 and 119?
What is the GCF of 52 and 109?
What is the GCF of 17 and 5?