What is the greatest common factor of 42 and 84?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 42 and 84. To solve this, we will identify the factors of both numbers and determine the largest factor they have in common.
Answer
The GCF of 42 and 84 is $42$.
Answer for screen readers
The greatest common factor (GCF) of 42 and 84 is 42.
Steps to Solve
- List the factors of each number
Start by finding all the factors for 42 and 84.
- The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
- The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Identify the common factors
Next, we will determine which factors are common to both lists.
- Common factors of 42 and 84 are: 1, 2, 3, 6, 7, 14, 21, 42
- Find the greatest common factor
Now, we will select the largest number from those common factors.
- The greatest common factor of 42 and 84 is 42.
The greatest common factor (GCF) of 42 and 84 is 42.
More Information
The greatest common factor is important for simplifying fractions and can help in solving problems involving ratios and proportions. Knowing the GCF can also be helpful in various applications in number theory.
Tips
- A common mistake is to overlook factors that appear in one number but not the other. It's important to list all factors thoroughly to ensure all common factors are counted.
- Another mistake is to incorrectly identify the largest common factor. Always double-check by comparing the common factors list.
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