Posted on January 17th, 2007 by Christian López Espínola "penyaskito"
Visto en Flicker, en el grupo de Múltiplos de 37:
Here’s a simple trick, very similar to the trick for telling if a number is divisible by 9 (adding up the digits). If you can do some simple arithmetic in your head, you don’t even need a calculator!
PART 1: NUMBERS UNDER 1000
For these, memory is your friend. There are only 27 numbers to remember, and there are also some really easy patterns that help you out.
First of all, observe that 111, 222, 333, …, 999 are all multiples of 37. (How cool is that?) Toss in zero to that mix, and then throw in all the numbers you can get by adding or subtracting 37 to these. From 0 you get 37. From 111 you get 74 and 148. From 222 you get 185 and 259. From 333 you get 296 and 370. And so on.
That’s all of them!
There’s one more trick that can help: If you take any of the above numbers and rotate its digits, you get another one of these numbers. In other words, if you have a 3-digit number that you KNOW is a multiple, then you automatically know two more as well. Try it: Starting with 74 (but take it as a 3-digit number, 074), you get 740 (which is also 777 – 37) and 407 (which is 444 – 37). It’s like a backup plan for confirming your mathin’.
PART 2: NUMBERS 1000 AND GREATER
- Divide the number up 3 digits at a time, starting from the right. If the last (leftmost) chunk has only 1 or 2 digits, that’s ok.
- Add up all the parts.
- Repeat the process until the sum is under 1000.
- Use the test in PART 1. If the sum is a multiple of 37, then so is the original number; and conversely, if the sum is not, then the original is not.
Filed under: Frikadas | Tagged: Math |