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