What is the GCF of 6 and 42?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 6 and 42. To solve this, we will identify the factors of both numbers and determine the largest factor they have in common.
Answer
The GCF of 6 and 42 is $6$.
Answer for screen readers
The greatest common factor (GCF) of 6 and 42 is $6$.
Steps to Solve
- List the factors of 6
To find the factors of 6, we identify the numbers that can be multiplied together to equal 6. The factors are: 1, 2, 3, 6
- List the factors of 42
Next, we do the same for 42. The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
- Identify common factors
Now, we will compare the lists of factors we found for both numbers. The common factors of 6 and 42 are: 1, 2, 3, 6
- Determine the greatest common factor
Finally, we analyze the common factors and find the greatest one. Among the common factors (1, 2, 3, 6), the greatest is: 6
The greatest common factor (GCF) of 6 and 42 is $6$.
More Information
The greatest common factor is useful in simplifying fractions and finding common denominators. In this case, 6 is not only a factor of both numbers but also the largest that divides both evenly.
Tips
A common mistake is to confuse factors with multiples. Ensure you list factors, which are the numbers that divide evenly into the original number, rather than the numbers produced by multiplying the original number.
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