The Secret of 73

[Mental Math]

Let’s have a game.

 

For this trick, secretly write 73 on a piece of paper, fold it up, and give to an unsuspecting friend.

1. Now have your friend select a four-digit number whatever (say, 3125) and enter it twice into a calculator. (31253125)
2. Announce that the number is divisible by 137 and have him verify it on his calculator.
3. Next, announce that he can now divide by his original four-digit number. After he has done so, dramatically command him to look at your prediction on the paper. It will match his calculator display: 73!

Want to know the simple math behind this "TRICK"?

[John Cuthber]

I tried calculating 73! but it's too big for my calculator.

 

I think you could do the same trick in binary, but you need to get them to choose 5 digit numbers and the corresponding "magic" numbers are 11 and 1011.

[TonyMcC]

 

The secret lies in the fact that if you divide the 8 digit number by the 4 digit number you always get 10001. If you divide this by 137 you always get 73. This gives the the 8 digit number 137 as one of its factors.( 8digit number = 4digit number * 137* 73 )

 

 

Used spoiler because OP seems to ask if we can work out what he knows.

Edited February 5, 2012 by TonyMcC