What is the maximum number of students among whom 63 pens and 140 copiescan be distributed in such a way that each student gets the same number of pens and same number of exercise books?

Options

A. 5
B. 2
C. 7
D. 3

Answer

To find the maximum number of students among whom 63 pens and 140 copies can be distributed such that each student gets the same number of pens and the same number of copies, we need to determine the greatest common divisor (GCD) of the two numbers (63 and 140).

### Step-by-Step Solution:

1. **Identify the Numbers**: We have 63 pens and 140 copies.

2. **Find the Prime Factorization**:
- For 63:
- 63 = 3 × 21
- 21 = 3 × 7
- So, the prime factorization of 63 is \(3^2 \times 7^1\).
- For 140:
- 140 = 2 × 70
- 70 = 2 × 35
- 35 = 5 × 7
- So, the prime factorization of 140 is \(2^2 \times 5^1 \times 7^1\).

3. **Identify Common Factors**:
- The common prime factor between 63 and 140 is 7.

4. **Determine the GCD**:
- The GCD is found by taking the lowest power of all common prime factors.
- Here, the only common prime factor is 7, and its lowest power is \(7^1\).
- Therefore, GCD(63, 140) = 7.

5. **Conclusion**: The maximum number of students that can receive pens and copies equally is 7.

### Final Answer:
The maximum number of students is **7**.