greatest common factor of 28 and 84
Understand the Problem
The question is asking us to find the greatest common factor (GCF) of the numbers 28 and 84. The GCF is the largest positive integer that divides both numbers without leaving a remainder.
Answer
$28$
Answer for screen readers
The greatest common factor (GCF) of 28 and 84 is $28$.
Steps to Solve
- List the factors of each number
First, we find the factors of 28 and 84.
- The factors of 28 are (1, 2, 4, 7, 14, 28).
- The factors of 84 are (1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84).
- Identify the common factors
Next, we look for the numbers that appear in both lists of factors.
The common factors of 28 and 84 are (1, 2, 4, 7, 14, 28).
- Find the greatest common factor
Now, we determine which of the common factors is the largest.
The greatest common factor from the list (1, 2, 4, 7, 14, 28) is (28).
The greatest common factor (GCF) of 28 and 84 is $28$.
More Information
The greatest common factor is useful in simplifying fractions and finding common denominators. In this case, 28 is not only a factor of both numbers but also confirms that they have a significant commonality.
Tips
- A common mistake is to skip listing all the factors and instead try to do a quick guess which may lead to incorrect conclusions. Always ensure to list all factors clearly.
- Another mistake can be overlooking smaller common factors. Check carefully for all common factors before identifying the GCF.
AI-generated content may contain errors. Please verify critical information
