What is the GCF of 30 and 36?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the two numbers, 30 and 36. To solve this, we will identify the factors of both numbers and find the largest one that they share.
Answer
$6$
Answer for screen readers
The greatest common factor (GCF) of 30 and 36 is $6$.
Steps to Solve
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Find the factors of 30
The first step is to identify all the factors of the number 30. The factors are the numbers that divide 30 without leaving a remainder.
The factors of 30 are:
1, 2, 3, 5, 6, 10, 15, 30 -
Find the factors of 36
Next, we need to find all the factors of 36 in the same way.
The factors of 36 are:
1, 2, 3, 4, 6, 9, 12, 18, 36 -
Identify the common factors
Now we compare the factors of 30 and 36 to find the common ones:
- Common factors:
1, 2, 3, 6
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Determine the greatest common factor (GCF)
Finally, we look for the largest number in the list of common factors.
The greatest common factor of 30 and 36 is:
$$ GCF = 6 $$
The greatest common factor (GCF) of 30 and 36 is $6$.
More Information
The GCF is useful in simplifying fractions and solving problems involving ratios. Understanding this concept can aid in various mathematical operations and real-life applications, such as dividing resources equally.
Tips
- Forgetting to list all factors accurately can lead to an incorrect GCF.
- Only considering one number's factors without comparing with the other number.
