Question

The number $4a6$ is divisible by 3. Find the least value of $a$.

Answer 1

For a number to be divisible by 3, the sum of all the digits of the number should be divisible by 3.
The number given is $4a6$.

$\Rightarrow$ Sum of digits = 4 + $a$ + 6
= 10 + $a$
$\Rightarrow$ Sum of digits is divisible by 3
$\therefore$ 10 + $a$ is divisible by 3
[1.5 marks]
The smallest multiple of 3 which is greater than 10 is 12.
$\Rightarrow$ 10 + $a$ = 12
$\Rightarrow$ $a$ = 12 - 10
$\therefore$ $a$ = 2
[ 1.5 marks ]

Therefore, the least value of a is 2.