The nearest integer to 6650 which is exactly divisible by 429 is

6864

The correct answer is Option (1) → 6864

1. Divide 6650 by 429 to find the quotient:

$6650 \div 429 \approx 15.501$

2. Find the two surrounding multiples:

• Lower Multiple: Multiply 429 by the whole number part (15).

$429 \times 15 = 6435$

• Upper Multiple: Multiply 429 by the next whole number (16).

$429 \times 16 = 6864$

3. Compare the distances from 6650:

• Distance to 6435: $6650 - 6435 = 215$
• Distance to 6864: $6864 - 6650 = 214$

Conclusion:

Since 214 is smaller than 215, the integer 6864 is closer to 6650.