What is the greatest common factor of 27, 12, and 21?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 27, 12, and 21. To solve this, we will determine the factors of each number and identify the largest factor that is common to all three.
Answer
The greatest common factor of 27, 12, and 21 is $3$.
Answer for screen readers
The greatest common factor of 27, 12, and 21 is $3$.
Steps to Solve
-
Find the factors of each number
- The factors of 27 are: $1, 3, 9, 27$
- The factors of 12 are: $1, 2, 3, 4, 6, 12$
- The factors of 21 are: $1, 3, 7, 21$
-
Identify common factors
Look for factors that are present in all three lists:
- Common factors are: $1, 3$
-
Determine the greatest common factor
From the common factors identified, the greatest one is:
- The GCF is $3$
The greatest common factor of 27, 12, and 21 is $3$.
More Information
The concept of the greatest common factor (GCF) is essential in simplifying fractions and finding common denominators. The GCF can also help in solving problems that involve multiple numbers, ensuring numbers can be divided evenly.
Tips
- Missing Factors: Sometimes, factors might be forgotten or overlooked. To avoid this, systematically list all factors for each number.
- Confusing GCF with LCM: Ensure you understand the difference between greatest common factor (GCF) and least common multiple (LCM). GCF finds the largest factor, while LCM finds the smallest multiple.
