What is the greatest common factor of 24 and 45?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 24 and 45. To find the GCF, we will identify the factors of both numbers and determine the largest factor that they have in common.
Answer
3
Answer for screen readers
The greatest common factor (GCF) of 24 and 45 is 3.
Steps to Solve
- List the Factors of 24
Start by identifying all the factors of the number 24.
The factors can be found by dividing 24 by all integers up to its square root.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.
- List the Factors of 45
Next, identify all the factors of the number 45.
The factors of 45 are: 1, 3, 5, 9, 15, 45.
- Identify Common Factors
Now, we need to determine the common factors between 24 and 45 by comparing the two lists of factors found in previous steps.
Common factors are: 1, 3.
- Find the Greatest Common Factor
The last step is to find the greatest of the common factors identified.
The greatest common factor (GCF) is: 3.
The greatest common factor (GCF) of 24 and 45 is 3.
More Information
The GCF is the largest number that divides both numbers without leaving a remainder. Knowing how to find the GCF is useful in simplifying fractions and in various applications of number theory.
Tips
- One common mistake is forgetting to list all factors. Always ensure you check each number up to the square root.
- Another mistake is misidentifying common factors due to not comparing both factor lists carefully.
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