What is a number that can divide exactly into two or more different numbers called?

A number that can divide exactly into two or more different numbers is known as a common factor. This means that if you take two or more numbers, the common factor is one that divides each of those numbers without leaving a remainder. For instance, in the case of the numbers 6 and 12, the factors of 6 are 1, 2, 3, and 6, while the factors of 12 are 1, 2, 3, 4, 6, and 12. The numbers 1, 2, 3, and 6 are common factors of both 6 and 12, demonstrating that they can all divide both numbers evenly.

In addition to common factors, there are other related concepts, such as common multiples, which pertain to numbers that can be formed by multiplying a common number across different values. Divisors are simply numbers that can divide another number, but they do not specifically denote that they must apply to multiple numbers simultaneously. Meanwhile, prime factors refer to prime numbers that can only divide another number evenly, emphasizing the properties of primality rather than their commonality across multiple numbers. Understanding this distinction helps to clarify the mathematical relationships among different numbers.