Question

On dividing 30879 by a certain number, the quotient is 67 and the remainder is 327. Find the divisor.

• A. \(476 \)
• B. \(456 \)
• C. \(466 \)
• D. \(444 \)
• E. \(457 \)

Hint:

Always use: \[ \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \] Rearrange carefully to find missing values.

Answer 1

The Correct Option is A

Concept: Division algorithm: \[ \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \]
Step 1: Substitute given values.
\[ 30879 = \text{Divisor} \times 67 + 327 \]

Step 2: Rearrange to find divisor.
\[ 30879 - 327 = \text{Divisor} \times 67 \] \[ 30552 = \text{Divisor} \times 67 \]

Step 3: Solve for divisor.
\[ \text{Divisor} = \frac{30552}{67} = 456 \]