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Seven and Thirteen
Thanks Bob K

Find a calculator and a friend.

Ask a friend to select a three-digit number and enter it twice into the calculator.
Example : 345345

Ask your friend to divide this number by 11.
Example : 345345 / 11 = 31395

Now ask you friend to divide the result by 13.
Example : 31395 / 13 = 2415

Ask your friend to divide this answer by the original three-digit number.
Example : 2415 / 345 = 7

Now magically tell your friend that the answer is 7

To change the final answer to 13, tell your friend to divide by 7 in step 3.
Example :  31395 / 7 = 4485
4485 / 345 = 13

Why this happens :

Entering a three-digit number twice (345345) is equivalent to multiplying it by 1001. (345 x 1001 = 345,345).
Since 1001 = 7 x 11 x 13, the six-digit number will be divisible by 7, 11, 13.

 PS :  Try more math tricks here.