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← 02-03 Divisible By Five Solution

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Showing Revision 1 created 07/07/2012 by Amara Bot.

  1. Okay, how did you solve the problem?
  2. The naive or straightforward or brute force way of solving this problem
  3. is to actually take all of these numbers, multiply them together, divide that answer by 5,
  4. and see what the remainder is. If the remainder is 0, then it is divisible by 5.
  5. Otherwise, it's not. But you would be very silly to go through that.
  6. What you should do is realize that a product is going to be divisible by 5
  7. if and only if one of the number that you're multiplying into the product is divisible by 5.
  8. And a number is divisible by 5 if and only if its last digit is a 0 or a 5.
  9. What you can do now, instead of actually doing any multiplying,
  10. you just scan your eyes down the columns here and notice that most of them are not 0s or 5s,
  11. but if you're eagle-eyed, you would have noticed this.
  12. There's one number in there that's divisible by 5--945--
  13. and that's all it takes. The whole product is now going to be divisible by 5.
  14. The answer we're looking for is yes. The product is divisible by 5. Ta da!