What is the GCF of 16 and 64?
Understand the Problem
The question is asking to find the greatest common factor (GCF) of the numbers 16 and 64. The GCF is the largest positive integer that divides both numbers without leaving a remainder.
Answer
The greatest common factor (GCF) of 16 and 64 is $16$.
Answer for screen readers
The greatest common factor (GCF) of 16 and 64 is $16$.
Steps to Solve
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List the factors of each number Determine the factors of 16 and 64 by identifying all positive integers that divide each number.
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 64: 1, 2, 4, 8, 16, 32, 64
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Identify the common factors Look for the factors that are common to both lists of factors found in the previous step.
- Common factors: 1, 2, 4, 8, 16
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Find the greatest common factor Select the largest number from the list of common factors.
Therefore, the greatest common factor of 16 and 64 is 16.
The greatest common factor (GCF) of 16 and 64 is $16$.
More Information
The greatest common factor is an important concept in number theory, often used in simplifying fractions and finding equivalent ratios. In this case, since 64 is a multiple of 16, we clearly see that 16 divides both numbers evenly.
Tips
- Confusing GCF with LCM (Least Common Multiple): Always remember GCF is the largest factor common to both numbers, while LCM is the smallest multiple common to both.
- Not checking all factors: Ensure you list all factors of each number to accurately identify the common factors.
