In a division problem with zero remainder, a student used 12 as the divisor instead of 21 and got a quotient of 35. What is the correct quotient?

Given data

• True division has remainder 0.
• Correct divisor = 21.
• Student mistakenly used divisor = 12 and obtained quotient = 35.

Concept / Approach

• If the true remainder is 0, the dividend must be an exact multiple of the correct divisor (21).
• The student's calculation tells us the dividend also equals 12 × 35 (since a quotient of 35 was obtained).

Step-by-step calculation
Dividend from mistaken work = 12 × 35 = 420Check with the true divisor: 420 ÷ 21 = 20 (remainder 0)

Verification
Since the problem states the remainder is 0 in the correct setup, 420 being exactly divisible by 21 confirms consistency.

Common pitfalls

• Forgetting that a zero remainder forces the dividend to be a multiple of the correct divisor.
• Trying to adjust the quotient proportionally without first finding the actual dividend.

Final Answer
20