On dividing $15968$ by a certain number, the quotient is $89$ and the remainder is $37$. Find the divisor.

### Concept & Formula The problem relies on the fundamental division algorithm, which relates the four components of division: $$ \text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder} $$ ### Step-by-Step Solution **Given:** * Dividend = $15968$ * Quotient = $89$ * Remainder = $37$ **Calculation / Deduction:** * We need to isolate the Divisor. Rearranging the division formula: $$ \text{Divisor} = \frac{\text{Dividend} - \text{Remainder}}{\text{Quotient}} $$ * Substitute the given values into the formula: $$ \text{Divisor} = \frac{15968 - 37}{89} $$ * Subtract the remainder from the dividend: $$ \text{Divisor} = \frac{15931}{89} $$ * Perform the division: $15931 \div 89 = 179$. ### Exam Strategy & Shortcut To avoid long division, use the unit digit method to identify the correct option. The numerator $15931$ ends in $1$. The denominator $89$ ends in $9$. You need a number that, when multiplied by $9$, gives a unit digit of $1$. Since $9 \times 9 = 81$, the divisor must end in $9$. If only one option ends in $9$, pick it instantly. If multiple do, use quick approximation ($16000 \div 90 \approx 177$), pointing directly to $179$. ### Common Pitfall A common mistake is forgetting to subtract the remainder before dividing (i.e., doing $15968 \div 89$), which will result in a messy decimal and cause confusion during the exam. ### Final Answer Therefore, the correct answer is 179.