Find the GCF (greatest common factor) of 18 and 11.

Find the GCF (greatest common factor) of 18 and 11.

The Correct Answer and Explanation is:

The greatest common factor (GCF) of two numbers is the largest number that divides both of them exactly without leaving a remainder.

Step 1: List the factors of 18 and 11

Factors of 18:

• 1, 2, 3, 6, 9, 18

Factors of 11:

• 1, 11

Step 2: Identify the common factors

Looking at the factors of both 18 and 11, we see that the only common factor is 1.

Step 3: Conclusion

Since 1 is the only common factor, the GCF of 18 and 11 is 1.

Explanation:

The GCF is a key concept in number theory and is used in simplifying fractions, solving problems related to divisibility, and finding the simplest form of a ratio. In this case, since 18 and 11 are relatively prime (i.e., they do not share any other common factors except 1), their greatest common factor is 1.

This process involves understanding that when two numbers have no other common factors besides 1, they are termed “coprime.” For any pair of coprime numbers, the GCF will always be 1. This fact is fundamental to many areas of mathematics, particularly when dealing with prime numbers and simplifying fractions.