gcf of 21 and 27
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 21 and 27. To find the GCF, we need to identify the factors of both numbers and determine which is the largest one that they both share.
Answer
The greatest common factor (GCF) of 21 and 27 is $3$.
Answer for screen readers
The greatest common factor (GCF) of 21 and 27 is $3$.
Steps to Solve
- Identify the factors of 21
The factors of 21 are the numbers that can evenly divide 21. We can find these by listing them out:
- 1
- 3
- 7
- 21
So, the complete list of factors for 21 is: $1, 3, 7, 21$.
- Identify the factors of 27
Next, we do the same for 27. The factors of 27 are:
- 1
- 3
- 9
- 27
Thus, the complete list of factors for 27 is: $1, 3, 9, 27$.
- Compare the factors
Now we need to find the common factors between the two lists:
- Common factors of 21 and 27 are: $1, 3$.
- Find the greatest common factor
The greatest common factor (GCF) is the largest number in the list of common factors. From the common factors $1$ and $3$, the maximum number is: $$ \text{GCF} = 3 $$
The greatest common factor (GCF) of 21 and 27 is $3$.
More Information
The GCF is an essential concept in number theory and is often used in simplifying fractions, finding least common multiples, and solving problems involving divisibility. The largest number that divides both 21 and 27 without leaving a remainder is $3$.
Tips
- Forgetting to list all factors carefully. Ensure that every factor is included by checking each number against the original number.
- Misidentifying the greatest factor by overlooking smaller common factors. Always compare all common factors to find the largest one.
