What is the GCF of 84 and 28?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 84 and 28. To solve this, we will identify the factors of both numbers and determine the highest factor they share.
Answer
$14$
Answer for screen readers
The greatest common factor (GCF) of 84 and 28 is $14$.
Steps to Solve
- Identify the factors of each number
We start by finding the factors of 84 and 28.
For 84, we can list the factors:
- 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
For 28, we list the factors:
- 1, 2, 4, 7, 14, 28
- Find the common factors
Next, we look for the factors that 84 and 28 have in common.
Common factors from the lists:
- 1, 2, 4, 7, 14
- Determine the greatest common factor
Now we select the highest number from the common factors we identified.
The greatest common factor is:
- 14
The greatest common factor (GCF) of 84 and 28 is $14$.
More Information
The greatest common factor is the largest positive integer that divides both numbers without leaving a remainder. Understanding GCF is useful in simplifying fractions and in creating common denominators.
Tips
- A common mistake is to confuse GCF with the least common multiple (LCM). Remember that GCF finds the highest shared factor, while LCM finds the smallest number shared as a multiple.
- Another mistake is incorrectly identifying the common factors. Make sure to check all factors correctly.
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