On dividing 12401 by a certain number, we get 77 as quotient and 4 as remainder. What is the divisor?

Options

A. 161
B. 162
C. 163
D. 164

Explanation

To find the divisor in the given problem, we can use the division algorithm, which states:

\[ \text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder} \]

Given:
- Dividend (a) = 12401
- Quotient (q) = 77
- Remainder (r) = 4

We need to find the divisor (b).

### Step 1: Set up the equation using the division algorithm
Using the division algorithm, we can write:

\[ 12401 = b \times 77 + 4 \]

### Step 2: Rearrange the equation to isolate the term with the divisor
Subtract the remainder from both sides:

\[ 12401 - 4 = b \times 77 \]

This simplifies to:

\[ 12397 = b \times 77 \]

### Step 3: Solve for the divisor
Now, to find the divisor \( b \), divide both sides by 77:

\[ b = \frac{12397}{77} \]

### Step 4: Perform the division
Now we will perform the division:

1. Divide 12397 by 77.
2. Calculate how many times 77 fits into 12397.

After performing the division, we find:

\[ 12397 \div 77 = 161 \]

Thus, the divisor \( b \) is:

\[ b = 161 \]

### Final Answer
The divisor is **161**.

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