What are Multiples

Student: When we talk about multiples of whole numbers, do we just mean the times tables?

Mentor: Sort of. Let's use an example to get this idea straight.

Consider the number 3; what are the multiples of 3? The formal definition of a multiple of 3 is: any number that three divides evenly or any number for which 3 is a factor. For a number to be divided "evenly" by three the answer must be a whole number with no remainders. So, 27 is a multiple of 3 since 27 / 3 = 9 (9 is a whole number), but 25 is not since 25 / 3 = 8 + a remainder of 1.

Student: So anything in the 3 times table is going to be a multiple of 3. Are there other multiples of 3?

Mentor: What do you think? Can I have a number that is not in the 3 times table that has 3 as a factor?

Student: To have three as a factor, the number has to be equal to 3 times something, so I think all of the multiples of 3 are in the three times table.

Mentor: Good. Can you list part of the three times table?

Student: Sure:

          3 times 0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
 	  is      0   3   6   9  12  15  18  21  24  27  30  33  36  39  42  45