## Friday, February 24, 2006

### Random number

Try thinking out a random 3-digit number and writing it twice on a piece of paper, forming a 6-digit number (for example the number is 123, than you will have to put down 123123 on the paper). Now divide this 6-digit number by 7. There will be no remainder, I guarantee. Now divide the result by 11. No remainder again, I guarantee. Now divide the new result by 13. What happened?

1. Its the first 3 digits again. I love math tricks like this.

2. I thought, "Why?" So since dividing by all 3 numbers is the same as dividing by (7x11x13), I found that figure on a calculator:
1001. Intriguing. Let's see...
729729/1001... the long way:

729
1001 / 729729
7007
2902
2002
9009

It makes perfect sense when you see it that way... every number that you drop down makes the first and last digit the same (2902) so 1001 goes into it nicely without screwing up the subtraction for the next row (9009).

Pretty awesome, and an added bonus of coolness when 1001 is separated into three factors.

- Rachele

3. Awww, it didn't save my long division correctly...

Oh well, with a good imagination, or a piece of scrath paper, it can be deciphered. :)

- Rachele

4. Rachel, thanks for the great explanation! Mine isn't half as good.

Writing a 3-digit number twice is equivalent to multiplying it by 1001. Note that 7*11*13=1001.

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