What is the least value of K so that the numb | vedclass

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(A) number is divisible by $9$ if the sum of its digits is divisible by $9$.Sum of the digits of $6735K1 = 6 + 7 + 3 + 5 + K + 1 = 22 + K$.For the num

Vedclass · Accepted Answer

$5$

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(A) number is divisible by $9$ if the sum of its digits is divisible by $9$.Sum of the digits of $6735K1 = 6 + 7 + 3 + 5 + K + 1 = 22 + K$.For the number to be divisible by $9$,the sum $22 + K$ must be a multiple of $9$.The multiples of $9$ are $9, 18, 27, 36, \dots$.Since $K$ is a single digit $(0-9)$,$22 + K$ must be at least $22$ and at most $22 + 9 = 31$.The only multiple of $9$ in the range $[22, 31]$ is $27$.Therefore,$22 + K = 27$.$K = 27 - 22 = 5$.Thus,the least value of $K$ is $5$.

What is the least value of $K$ so that the number $6735K1$ is divisible by $9$?

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