When 616 is divided by a certain positive number which is 
66
2
23
%
 of the quotient it leaven 16 as the remainder .Find the divisor

Let's break down the problem step by step.

1. Let the divisor be \( D \).
2. According to the problem, when 616 is divided by \( D \), the remainder is 16.
   - Therefore, the quotient is \( Q = \frac{616 - 16}{D} = \frac{600}{D} \).
3. It is also given that the divisor \( D \) is 66\(\frac{2}{23}\)% of the quotient.

We first convert the percentage to a decimal:
\[
66\frac{2}{23}\% = \frac{1528}{23 \times 100} = \frac{1528}{2300} \approx 0.6643
\]

So, \( D = 0.6643 \times Q \).

4. Substitute \( Q = \frac{600}{D} \) into the equation:
\[
D = 0.6643 \times \frac{600}{D}
\]

5. Multiply both sides by \( D \) to clear the fraction:
\[
D^2 = 0.6643 \times 600
\]
\[
D^2 = 398.58
\]
\[
D = \sqrt{398.58} \approx 19.96 \approx 20
\]

So, the divisor \( D \) is approximately **20**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How is the remainder related to the divisor and quotient?
2. How do we handle problems involving percentages of unknown quantities?
3. What if the remainder was zero? How would that change the problem?
4. Can you explain the importance of remainders in division?
5. How does rounding impact the accuracy of mathematical results?

**Tip:** Always double-check calculations involving percentages and remainders, as small errors can lead to incorrect conclusions.

Learn how to find a divisor when given a division problem with a specific remainder. This problem involves understanding percentages of quotients and using basic division principles. Suitable for students in Grades 6-8.

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