Find the least value of k for which a 7-digit number 249k876 is divisible by 6.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 0.
Divisibility Rule for 6: A number is divisible by 6 if it is divisible by both 2 and 3.
Divisibility Rule for 2: A number is divisible by 2 if its last digit is even.
Divisibility Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
The last digit of 249k876 is 6, which is even.
So, the number is divisible by 2 regardless of the value of k.
Sum of the digits = 2 + 4 + 9 + k + 8 + 7 + 6 = 36 + k
To make the number divisible by 3, the sum (36 + k) must be divisible by 3
If k = 0 then 36 + k = 36 which is divisible by 3
Therefore, the least value of k is 0.