What is the greatest common factor of 64 and 32?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 64 and 32. To solve this, we will identify the factors of each number and determine the largest factor that they both share.
Answer
The greatest common factor (GCF) of 64 and 32 is $32$.
Answer for screen readers
The greatest common factor (GCF) of 64 and 32 is $32$.
Steps to Solve
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List the factors of 64 First, we need to find all the factors of 64. The factors of a number are all the integers that can divide the number without leaving a remainder. The factors of 64 are: $1, 2, 4, 8, 16, 32, 64$.
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List the factors of 32 Next, we will find all the factors of 32 in the same way. The factors of 32 are: $1, 2, 4, 8, 16, 32$.
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Identify the common factors Now we look for the factors that are common to both 64 and 32. The common factors are: $1, 2, 4, 8, 16, 32$.
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Find the greatest common factor Finally, we select the largest factor from the common factors we identified. The greatest common factor (GCF) is $32$.
The greatest common factor (GCF) of 64 and 32 is $32$.
More Information
The greatest common factor is an important concept in number theory and is useful in simplifying fractions and finding common denominators. In this case, both 64 and 32 are powers of 2, specifically $64 = 2^6$ and $32 = 2^5$, which makes it easier to find their GCF.
Tips
- Forgetting to list all the factors correctly can lead to an incorrect GCF. Make sure to double-check each factor.
- Assuming the GCF is always the smaller number without considering all factors.
