In math, factors and multiples are two important connected concepts. Multiplication and division are inverse operations. You may have noticed that, in math, you tend to run into the same ideas over and over again. For example, mathematicians have six different ways to talk about this relationship.
For example, the following equation is true:
So this equation using the inverse operation is also true:
The following three statements all focus on the relationship between 5 and 20 from the perspective of multiplication:
5 multiplied by some number is 20.
5 is a factor of 20.
20 is a multiple of 5.
In two of the examples, you can see this relationship reflected in the words multiplied and multiple. For the remaining example, keep in mind that two factors are multiplied to equal a product.
Similarly, the following three statements all focus on the relationship between 5 and 20 from the perspective of division:
20 divided by some number is 5.
20 is divisible by 5.
5 is a divisor of 20.
Why do mathematicians need all these words for the same thing? Maybe for the same reason that Eskimos need a bunch of words for snow. When you understand the concepts behind the words factor and multiple, which word you choose doesn't matter a whole lot.