Find the least value of k for which a 7-digit number 249k876 is divisible by 6.

Question

Accepted Answer

A number is divisible by 6 if it is divisible by both 2 and 3.

Step 1: Divisibility by 2
The last digit of the number must be even. Here, the last digit is 6, which is even, so the number is divisible by 2.

Step 2: Divisibility by 3
The sum of the digits must be divisible by 3.

Digits: 2, 4, 9, k, 8, 7, 6
Sum = 2 + 4 + 9 + k + 8 + 7 + 6 = 36 + k

We need (36 + k) to be divisible by 3.
Since 36 is divisible by 3, k must be divisible by 3.

Possible values of k (0 to 9) divisible by 3 are 0, 3, 6, 9.

From the options given (5, 0, 7, 1), only 0 is divisible by 3.

Therefore, the least value of k is 0.

Answer

Answer

Answer