What is the GCF of 72 and 84?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 72 and 84. To solve this, we will find the factors of both numbers and identify the largest factor that they share.
Answer
The greatest common factor of 72 and 84 is $12$.
Answer for screen readers
The greatest common factor (GCF) of 72 and 84 is 12.
Steps to Solve
- List the factors of each number
First, we need to determine the factors of both 72 and 84.
- The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
- 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 common factors between the two sets we listed.
The common factors of 72 and 84 are: 1, 2, 3, 4, 6, 12.
- Determine the greatest common factor (GCF)
Now, we find the largest number from the common factors found in the previous step.
The greatest common factor is 12.
The greatest common factor (GCF) of 72 and 84 is 12.
More Information
The GCF, or greatest common factor, indicates the largest number that divides both numbers evenly. It is useful in simplifying fractions and solving problems that involve ratios.
Tips
- Overlooking larger common factors: Sometimes, one might miss larger common factors if they don't check all factors thoroughly. To avoid this, ensure to list all factors or use the prime factorization method.
- Confusing GCF with LCM: GCF is often confused with the least common multiple (LCM). Remember that GCF finds the largest shared factor, while LCM finds the smallest multiple.
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