Greatest common factor for 45 and 30
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 45 and 30. To find the GCF, we can list the factors of each number and identify the largest factor they have in common.
Answer
$15$
Answer for screen readers
The greatest common factor (GCF) of 45 and 30 is $15$.
Steps to Solve
- List the factors of each number
First, we will find the factors of 45 and 30.
- The factors of 45 are: 1, 3, 5, 9, 15, 45
- The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
- Identify the common factors
Next, we will find the factors that are common to both numbers by comparing the lists we created.
- Common factors of 45 and 30 are: 1, 3, 5, 15
- Choose the greatest common factor
Now we will identify the largest number from the common factors we found.
- The greatest common factor is 15.
The greatest common factor (GCF) of 45 and 30 is $15$.
More Information
The greatest common factor is useful in simplifying fractions and solving problems involving ratios. The GCF can also help in finding out how many groups you can create or the largest pieces that can fit into both quantities evenly.
Tips
- Forgetting to list out all factors: Ensure all factors are accounted for when finding common ones.
- Confusing GCF with LCM (Least Common Multiple): Remember that GCF involves finding the largest factor, while LCM finds the smallest multiple.
