MATH SOLVE

3 months ago

Q:
# What is the GCF of 51 and 11?

Accepted Solution

A:

Solution: The GCF of 51 and 11 is 1
Methods
How to find the GCF of 51 and 11 using Prime Factorization
One way to find the GCF of 51 and 11 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 51?
What are the Factors of 11?
Here is the prime factorization of 51:
3
1
×
1
7
1
3^1 × 17^1
3 1 × 1 7 1
And this is the prime factorization of 11:
1
1
1
11^1
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 51 and 11 is 1.
Thus, the GCF of 51 and 11 is: 1
How to Find the GCF of 51 and 11 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 51 and 11 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, 51 and 11:
Factors of 51: 1, 3, 17, 51
Factors of 11: 1, 11
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 51 and 11 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 148 and 142?
What is the GCF of 56 and 112?
What is the GCF of 123 and 38?
What is the GCF of 50 and 32?
What is the GCF of 86 and 99?