What is the GCF of 12, 18, and 24?

Understand the Problem

The question is asking for the greatest common factor (GCF) of the numbers 12, 18, and 24. To solve this, we need to find the largest number that can divide all three of these numbers without leaving a remainder.

Answer

6

Steps to Solve

List the factors of each number
To find the GCF, we first need to identify the factors of each of the three given numbers.

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Identify the common factors
Next, we need to look for factors that are common to all three numbers we've listed.

Common factors: 1, 2, 3, 6

Find the greatest common factor
Finally, we'll determine which of the common factors is the greatest. From the list we found:

The greatest common factor is 6.

The greatest common factor (GCF) of 12, 18, and 24 is 6.

More Information

The greatest common factor (GCF) is useful in various mathematical applications, such as simplifying fractions or finding common denominators. The process of listing factors is foundational in number theory and helps in understanding divisibility.

Tips

Common mistakes include:

Not listing all factors properly, which can lead to missing common factors.
Confusing the greatest common factor with the least common multiple (LCM), which is a different concept.

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