On dividing `59761` by a certain number , the quotient is `189` and the remainder is `37`. Find the divisor.

Options

A. `322`
B. `316`
C. `206`
D. `346`

Answer

To find the divisor when dividing 59761 by a certain number, we can use the relationship between the dividend, divisor, quotient, and remainder. The formula we will use is:

**Dividend = (Divisor × Quotient) + Remainder**

Given:
- Dividend = 59761
- Quotient = 189
- Remainder = 37

We need to find the divisor. Let's denote the divisor as \( x \).

### Step-by-Step Solution:

1. **Set up the equation using the formula**:
\[ 59761 = (x \times 189) + 37 \]

2. **Subtract the remainder from the dividend**:
\[ 59761 - 37 = x \times 189 \]
\[ 59724 = x \times 189 \]

3. **Isolate the divisor \( x \)**:
To find \( x \), we need to divide both sides by 189:
\[ x = \frac{59724}{189} \]

4. **Perform the division**:
We can simplify the division:
- First, we can divide 59724 by 189.
- Let's calculate it step by step:
- 189 goes into 597 twice (since 189 × 3 = 567, which is less than 597).
- Subtract 567 from 597 to get 30.
- Bring down the next digit (2) to make it 302.
- 189 goes into 302 once (since 189 × 1 = 189).
- Subtract 189 from 302 to get 113.
- Bring down the next digit (4) to make it 1134.
- 189 goes into 1134 six times (since 189 × 6 = 1134).
- Subtract 1134 from 1134 to get 0.

Thus, we find:
\[ x = 316 \]

### Final Answer:
The divisor is **316**.

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