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

Question

Accepted Answer

To determine the divisor when dividing 15406 by a certain number, resulting in a quotient of 88 and a remainder of 6, we can use the formula for division:

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

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

Substituting these values into the formula, we have:

$$ 15406 = (\text{Divisor} \times 88) + 6 $$

To find the divisor, rearrange the equation:

$$ \text{Divisor} \times 88 = 15406 - 6 $$
$$ \text{Divisor} \times 88 = 15400 $$
$$ \text{Divisor} = \frac{15400}{88} $$

Calculating the division:

$$ \text{Divisor} = 175 $$

Thus, the divisor is 175, which corresponds to Option 4.

**Explanation for why each option is incorrect:**

1. **Option 1 (174):** If the divisor were 174, then:
   $$ 174 \times 88 + 6 = 15318 $$
   This does not equal 15406, so 174 is incorrect.

2. **Option 2 (147):** If the divisor were 147, then:
   $$ 147 \times 88 + 6 = 12942 $$
   This does not equal 15406, so 147 is incorrect.

3. **Option 3 (157):** If the divisor were 157, then:
   $$ 157 \times 88 + 6 = 13862 $$
   This does not equal 15406, so 157 is incorrect.

4. **Option 4 (175):** As calculated above, using 175 as the divisor:
   $$ 175 \times 88 + 6 = 15406 $$
   This matches the given dividend, confirming that 175 is indeed the correct divisor.

Therefore, Option 4 is the correct answer, as it satisfies the division equation perfectly.