What is the GCF of 36 and 84?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 36 and 84. To solve this, we can list the factors of each number and identify the largest factor they both share.
Answer
12
Answer for screen readers
The greatest common factor (GCF) of 36 and 84 is 12.
Steps to Solve
- List the factors of 36
To find the factors of 36, we can divide it by each integer from 1 up to 36 and list out the whole numbers that divide it without a remainder.
The factors of 36 are:
1, 2, 3, 4, 6, 9, 12, 18, 36
- List the factors of 84
Now, we do the same for 84 by dividing it by integers from 1 to 84.
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 factors that both numbers share in the lists we've created.
The common factors of 36 and 84 are:
1, 2, 3, 4, 6, 12
- Find the greatest common factor
Finally, we identify the largest number in the list of common factors, which gives us the GCF.
The greatest common factor is:
12
The greatest common factor (GCF) of 36 and 84 is 12.
More Information
The greatest common factor is useful in simplifying fractions and finding common denominators. Understanding how to find the GCF can be applied in various areas of mathematics, including solving problems related to ratios and proportional relationships.
Tips
- Failing to list all factors correctly: Be thorough when listing factors to ensure all possible values are found.
- Confusing GCF with least common multiple (LCM): Remember that GCF is the largest shared factor, while LCM is the smallest shared multiple.
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