Replace * by the smallest digit so that 723*56* is divisible by 6.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 2.
Divisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3.
Divisibility rule of 2: A number is divisible by 2 if its last digit is even or 0.
Divisibility rule of 3: A number is divisible by 3 if the sum of its digits is a multiple of 3.
723*56* is divisible by 2 if the last digit is even. Hence, it can be either 2 or 4. (from the options)
Take 4 as the smallest digit:
The sum of the digits of 7234564 = 31 (not divisible by 3)
Now, take 2 as the smallest digit:
The sum of the digits of 7232562 = 27 (Divisible by 3)
Hence, the smallest digit is 2.