What is the GCF of 48 and 64?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 48 and 64. To find the GCF, we will identify the largest number that divides both 48 and 64 without leaving a remainder.
Answer
$16$
Answer for screen readers
The greatest common factor (GCF) of 48 and 64 is $16$.
Steps to Solve
- List the factors of each number
First, find the factors of 48 and 64.
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 64 are: 1, 2, 4, 8, 16, 32, 64
- Identify the common factors
Next, identify the factors that are common to both sets.
The common factors of 48 and 64 are: 1, 2, 4, 8, 16
- Determine the greatest common factor
Now, find the greatest factor from the common factors.
The greatest common factor is 16.
The greatest common factor (GCF) of 48 and 64 is $16$.
More Information
The GCF is useful in simplifying fractions, finding common denominators, and is a crucial concept in number theory. GCF can also be found using prime factorization or the Euclidean algorithm.
Tips
- Not listing all factors: Always ensure you list all factors correctly.
- Confusing GCF with least common multiple (LCM): GCF is the largest number that divides both, whereas LCM is the smallest number that is divisible by both.
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