What is the GCF of 32 and 45?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 32 and 45. To find the GCF, we will determine the factors of both numbers and identify the largest factor they have in common.
Answer
The GCF of $32$ and $45$ is $1$.
Answer for screen readers
The greatest common factor (GCF) of $32$ and $45$ is $1$.
Steps to Solve
- List the factors of each number
First, we need to find all the factors of each number.
- For $32$: The factors are $1, 2, 4, 8, 16, 32$.
- For $45$: The factors are $1, 3, 5, 9, 15, 45$.
- Identify the common factors
Next, we identify the factors that are present in both lists.
From the factors we listed:
- Factors of $32$: $1, 2, 4, 8, 16, 32$
- Factors of $45$: $1, 3, 5, 9, 15, 45$
The only common factor is $1$.
- Determine the greatest common factor
Now, we find the greatest of the common factors. Since the only common factor is $1$, that is the greatest common factor.
The greatest common factor (GCF) of $32$ and $45$ is $1$.
More Information
The GCF is useful in simplifying fractions and finding common denominators. In this case, since $32$ and $45$ have no other factors in common, they are relatively prime, meaning their only common divisor is $1$.
Tips
- Not listing all factors: It's important to list all factors of both numbers to ensure no common factors are missed.
- Assuming without checking: One might assume the GCF is greater than $1$ without checking both lists of factors.
