What is the greatest common factor (GCF) of 8 and 12?

What is the greatest common factor (GCF) of 8 and 12?

• A. 2
• B. 3
• C. 4
• D. 6

Answer: (C)

To determine the greatest common factor (GCF) of 8 and 12, it's important to first find the factors of each number. The factors of 8 are 1, 2, 4, and 8. The factors of 12 are 1, 2, 3, 4, 6, and 12. The next step is to identify the common factors between the two sets. The common factors of 8 and 12 are 1, 2, and 4. Among these, the greatest one is 4, which means that 4 is the largest number that can divide both 8 and 12 without leaving a remainder. Understanding GCF is essential because it is a fundamental concept in number theory and is often used to simplify fractions, find equivalent fractions, and solve problems involving ratios. In this case, finding the GCF helps establish a foundational understanding of dividing quantities into equal parts.

To determine the greatest common factor (GCF) of 8 and 12, it's important to first find the factors of each number. The factors of 8 are 1, 2, 4, and 8. The factors of 12 are 1, 2, 3, 4, 6, and 12. The next step is to identify the common factors between the two sets. The common factors of 8 and 12 are 1, 2, and 4. Among these, the greatest one is 4, which means that 4 is the largest number that can divide both 8 and 12 without leaving a remainder.

Understanding GCF is essential because it is a fundamental concept in number theory and is often used to simplify fractions, find equivalent fractions, and solve problems involving ratios. In this case, finding the GCF helps establish a foundational understanding of dividing quantities into equal parts.