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Varvara

On dividing 2121 as well as 624 by a 3 digit number N, we get the same remainder. What is the sum of the digits of N?​

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Answer:

22

The symbol '' stands for the product of numbers.

We know that this equation is always true,

which is called the division algorithm. And,

  • is the dividend.
  • is the divisor.
  • is the quotient.
  • is the remainder.

Hence, we get two equations for ,

Subtracting two equations we get,

According to the division algorithm, 1497 is divided by without any remainder. Hence, is a factor of 1497.

The factorization of 1497 is .

For the factor, to be a three-digit,

The required number is 499. Hence, the sum of the three-digit number is 22.

Both numbers have the same remainder, 125. Hence, it is verified that is indeed 499.

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