Question

Write the smallest and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by $3$ :
a) _$6724$
b) $4765$_$2$

Answer 1

(a)

The number is given as $\_6724$.

The number is divisible by 3 if the sum of its digits is divisible by 3.

Adding the digits of the given number,

$6+7+2+4=19$

If 2 is added to the above number then the number will become 21 which is divisible by 3 and also, 2 is the smallest number that can fill the missing space.

Now, if 8 is added to the given number then the number will become 27 which is divisible by 3 and 8 is largest number that can make the given number divisible by 3.

Therefore, the smallest number will be 2 which will form $26724$ and the largest number will be 8 forming $86724$.

(b)

The number is given as $4765\_2$.

The number is divisible by 3 if the sum of its digits is divisible by 3.

Adding the digits of the given number,

$4+7+6+5+2=24$

If 0 is added to the above number then the number will become 24 which is divisible by 3 and also, 0 is the smallest number that can fill the missing space.

Now, if 9 is added to the given number then the number will become 33 which is divisible by 3 and 9 is largest number that can make the given number divisible by 3.

Therefore, the smallest number will be 0 which will form $476502$ and the largest number will be 9 forming $476592$.