What is the GCF of 72 and 90?
Understand the Problem
The question is asking us to determine the greatest common factor (GCF) of the numbers 72 and 90. The GCF is the largest number that divides both of these numbers without leaving a remainder.
Answer
$18$
Answer for screen readers
The greatest common factor (GCF) of 72 and 90 is $18$.
Steps to Solve
- List the factors of each number
First, we need to find all the factors of both 72 and 90.
For 72, the factors are:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
For 90, the factors are:
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- Identify the common factors
Next, we identify which factors are common to both lists.
The common factors are:
1, 2, 3, 6, 9, 18
- Determine the greatest common factor
Now, we find the largest number from the common factors identified in the previous step.
The greatest common factor from these is:
18
The greatest common factor (GCF) of 72 and 90 is $18$.
More Information
The greatest common factor is useful in simplifying fractions and finding common denominators. The GCF also has applications in algebra when factoring expressions.
Tips
- Forgetting to list all factors: Ensure you list each factor correctly.
- Not checking for the highest common factor: Always confirm you selected the greatest factor by comparing all common factors.
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