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

To find the nearest integer to 6650 that is exactly divisible by 429, divide 6650 by 429:

$6650 \div 429 = 15.501...$

This means 6650 is between the 15th and 16th multiples of 429.

The two nearest multiples of 429 are:

$429 \times 15 = 6435$

$429 \times 16 = 6864$

Calculate the distance from 6650 to each multiple:

Distance to 6435:

$6650 - 6435 = 215$

Distance to 6864:

$6864 - 6650 = 214$

Since $214 < 215$, the number 6864 is closer to 6650.

Therefore, the nearest integer to 6650 which is exactly divisible by 429 is 6864.