On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor?Options :A.163B.173C.183D.None of these

1. ### Break Down the Problem

To find the divisor in the division equation, we can use the formula: $\text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder}$ From the given information:

• Dividend = 12401
• Quotient = 76
• Remainder = 13

2. ### Relevant Concepts

Using the division formula, we will determine the divisor by rearranging the formula to solve for the divisor.

3. ### Analysis and Detail

We will plug in the known values into the division formula: $12401 = \text{Divisor} \times 76 + 13$ Now, simplifying the equation:

1. Subtract the remainder from the dividend: $12401 - 13 = \text{Divisor} \times 76$ $12388 = \text{Divisor} \times 76$
2. Now, divide both sides by 76 to find the divisor: $\text{Divisor} = \frac{12388}{76}$

4. ### Verify and Summarize

Now we perform the division: $\text{Divisor} = 163$ Therefore, the answer is verified as this matches one of the options provided.

Final Answer

The divisor is 163 (Option A).