Question

If the three digit number 20x is divisible by 9, find the smallest possible value of x.

Answer 1

For a number to be divisible by 9, the sum of its digits should be divisible by 9.
Hence for 20x to be divisible by 9, the value of 2 + 0 + x should be divisible by 9.
Then, 2 + x should be divisible by 9.

The smallest multiple of 9 which is greater than 2 is 9 itself.

$\Rightarrow$ x = 7

Therefore the smallest value of x for which the number 20x is divisible by 9 is 7.

Verification:
As we obtained the value of x as 7, the number is 207.
Sum of its digits = 2 + 0 + 7 = 9.
9 is divisible by 9.
Therefore, 207 is divisible by 9.
$(\frac{207}{9}=23)$