Tell students that you are going to test their division skills by doing the following experiment:

1. Pick any three-digit number that you wish.

2. Write it down then write it down again to make a six-digit number.
    For example, if you chose 428, then write down 428428.

3. Now divide this six-digit number by 7.   You shouldn't get a remainder.

4. Divide the quotient by 11, again you shouldn't get a remainder.

5. Divide that quotient by 13, and again you shouldn't get a remainder.

6. What is your answer?

How does it work?
You should get your original answer back.
When you formed the six digit number, you actually multiplied by 1,001.
The factors of 1,001 are 7, 11, and 13.