What is the greatest common factor of 36 and 33?
Understand the Problem
The question is asking to find the greatest common factor (GCF) of the numbers 36 and 33. The GCF is the largest number that divides both of these numbers without leaving a remainder.
Answer
The greatest common factor (GCF) of 36 and 33 is $3$.
Answer for screen readers
The greatest common factor of 36 and 33 is $3$.
Steps to Solve
- List the Factors of Each Number
First, find all the factors of the numbers 36 and 33.
For 36: The factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
For 33: The factors are 1, 3, 11, and 33.
- Identify Common Factors
Next, identify the factors that are common to both lists.
Common factors are: 1 and 3.
- Find the Greatest Common Factor
Determine the largest common factor from the list of common factors identified in the previous step.
The greatest common factor is 3.
The greatest common factor of 36 and 33 is $3$.
More Information
The greatest common factor (GCF) is useful in simplifying fractions and finding common denominators. Notably, the GCF of two prime numbers is always 1, while composite numbers like 36 and 33 can have larger GCF values.
Tips
- Not listing all factors: Make sure to list all factors for each number to accurately identify common ones.
- Overlooking common factors: Sometimes, it's easy to miss smaller factors, so double-check your lists.
- Confusing GCF with LCM: Remember, GCF is the largest number that divides both, whereas LCM (Least Common Multiple) is the smallest multiple they share.
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