In detail

Divide by five

Divide by five

The other day my math teacher wrote a four-digit number on the board, took the eraser and said I was able to divide it by five simply by erasing the thousands digit. Indeed, after deleting that digit the number was divided by five. And there is more, he said, I will divide it again by five by deleting the digit of hundreds. And indeed, after deleting that digit the number was divided by five again as if by magic.

Could you tell me what number you wrote on the board initially?

Solution

He initially wrote 1250. If we delete the digit of thousands we have 250 that is the fifth part of 1250. If we now eliminate the digit of hundreds, we have 50 left that is again the fifth part of 250.