In the following replace * by the smallest number so that the given number is divisible by the number mentioned:
$817 * 67$ by $11$ .

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Solution

Divisibility rule of $11$ - A number is divisible by $11$ if the difference of the sum of digits at even places and sum of digits at odd places is $0$ or a multiple of $11$ .
Sum of $8 + 7 + 6 = 21$
Sum of $1 + 7 = 8$
Difference $= 21 - 8 = 13$ . If we subtract $2$ from $13$ we will get $11$ which is a multiple of $11$ .
Therefore, $2$ is the smallest number that can replace $*$ in the given number making it divisible by $11$ .

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