Question

Find the largest three digit number which is divisible by 6.

• A. 999
• B. 998
• C. 997
• D. 996

Answer 1

The correct option is D 996

For a number to be divisble by 6 it has to be divisible by both 2 and 3.

$\Rightarrow$ The number should be an even number and sum of its digits should be divisible by 3.

The largest 3-digit number is 999.
It is not an even number. So, it is not divisible by 2 and hence not divisible by 6.

Consider 998.
It is an even number, so it is divisible by 2.
9 + 9 + 8 = 26 is not divisible by 3.
Hence, 998 is not divisible by 3.

997 is not an even number hence, it is not divisible by 6.

Consider 996.
It is an even number, so it is divisible by 2.
9 + 9 + 6 = 24 is divisible by 3.

Therefore, the largest three digit number which is divisible by 6 is 996.