Multiple choice

A number when divided by $136$, leaves $36$ as remainder. If the same number is divided by $17$, what will be the remainder?

  1. $0$
  2. $1$
  3. $2$
  4. $3$
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C Correct answer
Explanation

Number N = 136k + 36. To find N mod 17, note 136 = 17 * 8. So 136k is divisible by 17. N mod 17 = 36 mod 17 = 2.

AI explanation

Let the unknown number be N and the quotient be q, so by the division algorithm N equals 136 times q plus 36. Because 136 is exactly divisible by 17, the part 136 times q is completely divisible by 17. Divide the remainder 36 by 17 to get a new remainder of 2. The final remainder is 2.

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