What is the GCF of 11 and 33?

Understand the Problem

The question is asking for the greatest common factor (GCF) of the numbers 11 and 33. The GCF is the largest positive integer that divides both numbers without leaving a remainder.

Answer

The greatest common factor (GCF) of 11 and 33 is $11$.

Steps to Solve

Identify the Factors First, we need to find the factors of both numbers.

Factors of 11: $1, 11$
Factors of 33: $1, 3, 11, 33$

List Common Factors Next, we identify the common factors from the lists we made.

Common factors of 11 and 33 are: $1, 11$

Identify the Greatest Common Factor Now, we determine which of the common factors is the greatest.

The greatest common factor from our list of common factors is $11$.

The greatest common factor (GCF) of 11 and 33 is $11$.

More Information

The GCF is useful in simplifying fractions, finding common denominators, and various problems in number theory. In this case, since 11 is a prime number and it divides 33, it is the highest common factor.

Tips

A common mistake is forgetting to check all factors. It's important to list all factors of both numbers before determining the GCF.
Another mistake could be confusion over prime numbers; understanding that a prime number only has factors of 1 and itself is key.

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