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Find the divisor using the division algorithm where the division of 59761 yields the quotient 189 with a remainder 37.

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185

316

315

238

answer is B.

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Detailed Solution

The given data is as follows.
The division of 59761 yields the quotient 189 with a remainder 37.
As we know,

Dividend = Divisor × Quotient + Remainder

We assume that the divisor is x.
We shall perform the the calculation in the following way.

⇒ Divisor × Quotient + Remainder = Dividend ⇒ x × 189 + 37 = 59761 ⇒ 189 x = 59761 − 37 ⇒ 189 x = 59724 ⇒ x = 59724189

We shall now perform the long division in the following way.

18931659724 − 567 ¯ 302 − 189 ¯ 1134 − 1134 ¯ 0

Hence, we get the value of x.

⇒ x = 59724189 ⇒ x = 316

Therefore, the required divisor is 316 and, so the correct option is 2.

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