## Task 3 - V10823

In the number .378., the two dots are to be replaced by digits so that the resulting number is divisible by 72.

How did you determine the missing digits?
If a number is to be divisible by 72, it must also be divisible by 8 and 9, since $8 \cdot 9=72$. To determine the missing digits, one applies the divisibility rules of 8 and 9. One starts with the divisibility rule of 8, which gives the last digit of the number. 78. must therefore be divisible by 8. $720: 8=90$.

The number 64 is the only one between 60 and 70 that is divisible by 8. Therefore, the last digit must be 4.

To get the first digit, I apply the divisibility rule of 9. The sum of the known digits is $3+7+8+4=22$. The difference to 27, the next number divisible by 9, is 5. This is also the missing digit.

The complete number is 53784.