What is the greatest common factor?

The greatest common factor (GCF) refers to the largest number that can divide all of the given numbers without leaving a remainder. This definition is well captured in the correct answer, which emphasizes that the GCF is the largest factor common to all specified numbers.

When identifying the GCF, one lists the factors of each number and determines the highest value that appears in all lists. For instance, consider the numbers 12 and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12; the factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors are 1, 2, 3, and 6, with 6 being the greatest.

Understanding the GCF is essential for simplifying fractions, finding common denominators, and solving problems that require coordination of multiple quantities. This concept allows for efficient computation and clearer problem-solving strategies in more complex mathematical situations.

The other options do not correctly define or represent the concept of the greatest common factor. Instead, they describe different mathematical ideas that relate to numbers and their properties.