On dividing 15406 by a certain number the quotient is 88 and remainder 6. What is the divisor?

Options

A. 174
B. 147
C. 157
D. 175

Answer

To find the divisor when dividing 15406 by a certain number, we can use the relationship between the dividend, divisor, quotient, and remainder. The formula we will use is:

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

Given:
- Dividend = 15406
- Quotient = 88
- Remainder = 6

We can rearrange the formula to solve for the divisor:

\[ \text{Divisor} = \frac{\text{Dividend} - \text{Remainder}}{\text{Quotient}} \]

Now, let's substitute the values into the formula:

1. Calculate the value of \( \text{Dividend} - \text{Remainder} \):
\[ 15406 - 6 = 15300 \]

2. Now, divide this result by the quotient:
\[ \text{Divisor} = \frac{15300}{88} \]

3. Perform the division:
\[ 15300 \div 88 = 174.3181 \text{ (approximately)} \]

Since we need the exact divisor, we can calculate it as follows:
\[ \text{Divisor} = 174 \]

Thus, the divisor is:
\[ \text{Divisor} = 175 \]

### Final Answer:
The divisor is **175**.