What is the GCF of 18 and 72?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the two numbers 18 and 72. To find the GCF, we need to determine the largest number that divides both 18 and 72 without leaving a remainder.
Answer
$18$
Answer for screen readers
The greatest common factor (GCF) of 18 and 72 is $18$.
Steps to Solve
- List the Factors of Each Number
Start by finding all the factors of 18 and 72.
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Identify the Common Factors
Next, we find the common factors between the two lists.
- Common factors of 18 and 72: 1, 2, 3, 6, 9, 18
- Determine the Greatest Common Factor
From the list of common factors, identify the greatest one.
- The greatest common factor is 18.
The greatest common factor (GCF) of 18 and 72 is $18$.
More Information
The GCF helps in simplifying fractions, factoring polynomials, and finding least common multiples. It is a fundamental concept in number theory and is often used in various mathematical applications.
Tips
- Forgetting to list all factors properly or missing some factors can lead to incorrect results.
- Not checking all common factors before identifying the greatest one can also cause errors.
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