GCF of 16 and 81
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 16 and 81. This requires finding the largest number that divides both 16 and 81 without leaving a remainder.
Answer
$1$
Answer for screen readers
The greatest common factor of 16 and 81 is $1$.
Steps to Solve
- List the factors of each number
To find the greatest common factor (GCF) of 16 and 81, we start by listing the factors of each number.
Factors of 16: 1, 2, 4, 8, 16
Factors of 81: 1, 3, 9, 27, 81
- Identify the common factors
Next, we identify the factors that appear in both lists.
From the factors listed:
- The factors of 16 are: {1, 2, 4, 8, 16}
- The factors of 81 are: {1, 3, 9, 27, 81}
The common factor in both lists is: 1
- Determine the greatest common factor
Finally, we find the largest factor that is common to both numbers.
Since the only common factor is 1, the GCF is:
$$ \text{GCF}(16, 81) = 1 $$
The greatest common factor of 16 and 81 is $1$.
More Information
The greatest common factor is useful in various mathematical contexts, such as simplifying fractions or solving problems involving divisibility. In this case, since 16 and 81 have no other common factors, their GCF is 1, indicating they are relatively prime.
Tips
- A common mistake is to assume that two numbers must have factors other than 1. If two numbers share no common factors besides 1, they are considered relatively prime.
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