What is the greatest common factor of 18 and 32?
Understand the Problem
The question is asking for the greatest common factor (GCF) of two numbers, 18 and 32. To find the GCF, we will need to identify the factors of both numbers and determine which factor is the largest that divides both numbers evenly.
Answer
$2$
Answer for screen readers
The greatest common factor (GCF) of 18 and 32 is $2$.
Steps to Solve
- Identify the factors of 18
The factors of 18 are numbers that divide it evenly. We find them by checking each number from 1 to 18:
- 1, 2, 3, 6, 9, 18
So, the factors of 18 are: $1, 2, 3, 6, 9, 18$.
- Identify the factors of 32
Similarly, we find the factors of 32 by checking each number from 1 to 32:
- 1, 2, 4, 8, 16, 32
So, the factors of 32 are: $1, 2, 4, 8, 16, 32$.
- Find the common factors
Now, we look for factors that are present in both lists of factors:
- Common factors of 18 and 32 are: $1, 2$.
- Determine the greatest common factor
From the common factors, we have $1$ and $2$. The greatest of these is: $$ \text{GCF} = 2 $$
The greatest common factor (GCF) of 18 and 32 is $2$.
More Information
The GCF is useful in various applications, including simplifying fractions and finding common denominators for addition or subtraction of fractions. It’s a key concept in number theory.
Tips
- Listing non-factors: Sometimes, students might include numbers that do not divide evenly into the original numbers. Always check divisibility properly.
- Omitting common factors: Ensure you compare both lists thoroughly to find all common factors.
