FTCE General Knowledge Math Practice Test

Which of the following represents the definition of GCF?

1. The smallest whole number that can divide another number

2. The biggest prime factor of a number

3. The largest number that can divide two or more numbers evenly

4. The product of two or more numbers

The correct answer is: The largest number that can divide two or more numbers evenly

The definition of the greatest common factor (GCF) revolves around its role in identifying common divisors among a set of numbers. The GCF is specifically the largest integer that can exactly divide each of the numbers in a specified set without leaving a remainder. For instance, if you consider the numbers 12 and 18, the factors of these two numbers are 1, 2, 3, 4, 6, and 12 for 12, and 1, 2, 3, 6, 9, and 18 for 18. The common factors are 1, 2, 3, and 6, with 6 being the greatest of these; thus, it is the GCF of both numbers. The other choices do not accurately represent what GCF means. The first choice describes a concept that might relate to factors in general but does not specify the need for it to be the largest among common factors. The second choice addresses prime factors but does not convey the requirement for factors to be shared among multiple numbers. The last choice mistakenly describes the GCF as a product rather than discussing divisibility among integers. Thus, the description of the GCF as the largest number that