Question

find the value of K where 31k2 is divisible by 6​

Answer 1

Answer:

The value of k could be 0, 3, 6 or 9.

Explanation:

Divisibility by 6 : If a number is divisible by both 2 and 3, then the number is also divisible by 6.

First, let us know the divisibility by 2 and 3, If the number satisfies both, then it's surely divisible by 6.

Divisibility by 3: Sum of all the numbers in the digit should be divisible by 3.

Divisibility by 2: Unit digit of the number should be even.

Given that : 31k2 is divisible by 6

For this to be true 3 + 1 + k + 2 or 6 + k should be divisible by 3

⟹ 6 + k = 3

⟹ k = 3 - 6

⟹ k = -3

( it's not possible, value should be positive)

OR

⟹ 6 + k = 6

⟹ k = 6 - 6

⟹ k = 0

( possible )

OR

⟹ 6 + k = 9

⟹ k = 9 - 6

⟹ k = 3

( possible )

OR

⟹ 6 + k = 12

⟹ k = 12 - 6

⟹ k = 6

( possible )

OR

⟹ 6 + k = 15

⟹ k = 15 - 6

⟹ k = 9

( possible )

OR

⟹ 6 + k = 18

⟹ k = 18 - 6

⟹ k = 12

(not possible as it should be only a single digit )

From error and trial, we get the values of k = 0, 3,6 or 9