GCF of 24 and 96
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 24 and 96. To find the GCF, we can determine the factors of both numbers and identify the largest factor that they share.
Answer
$24$
Answer for screen readers
The greatest common factor (GCF) of 24 and 96 is $24$.
Steps to Solve
- Find the factors of 24
Start by listing all the factors of 24. Factors are numbers that can be multiplied together to get 24.
The factors of 24 are: $$ 1, 2, 3, 4, 6, 8, 12, 24 $$
- Find the factors of 96
Next, list the factors of 96 in the same way.
The factors of 96 are: $$ 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 $$
- Identify the common factors
Now we need to find the factors that both numbers share. By comparing both lists, we find:
The common factors of 24 and 96 are: $$ 1, 2, 3, 4, 6, 8, 12, 24 $$
- Determine the greatest common factor
Finally, identify the largest number in the common factors list. The greatest common factor (GCF) of 24 and 96 is:
$$ \text{GCF} = 24 $$
The greatest common factor (GCF) of 24 and 96 is $24$.
More Information
The greatest common factor helps in simplifying fractions and many other mathematical applications, like finding equivalent ratios. Understanding how to find the GCF is also useful in number theory and factoring polynomials.
Tips
- Forgetting to list out all factors or missing some factors can lead to an incorrect GCF.
- Confusing the concept of GCF with least common multiple (LCM) can also cause errors. Always ensure you are looking for factors, not multiples.
