What is the GCF of 9 and 21?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 9 and 21. To find the GCF, we need to identify the largest number that divides both 9 and 21 without leaving a remainder.
Answer
The greatest common factor (GCF) is $3$.
Answer for screen readers
The greatest common factor (GCF) of 9 and 21 is $3$.
Steps to Solve
- List the factors of each number
To find the GCF, we first list all the factors of both numbers.
Factors of 9:
- 1, 3, 9
Factors of 21:
- 1, 3, 7, 21
- Identify the common factors
Next, we identify which factors are common to both sets.
Common factors of 9 and 21:
- 1, 3
- Determine the greatest common factor
Now, we take the largest factor from the common factors identified.
The largest common factor is:
- 3
The greatest common factor (GCF) of 9 and 21 is $3$.
More Information
The GCF is useful in various mathematical applications such as simplifying fractions and finding equivalent ratios. Knowing how to determine the GCF can help with solving problems in number theory as well.
Tips
- Overlooking a factor: Sometimes, one might forget to list all factors. Always double-check by systematically listing them.
- Confusing GCF with LCM: Make sure to distinguish between the greatest common factor and the least common multiple (LCM). GCF looks for common factors, while LCM finds multiples.
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