The number nearest to 7658 and exactly divisible by 45 is:

The correct answer is 7650.

To find the number nearest to 7658 that is exactly divisible by 45, we first divide 7658 by 45 to find the remainder.

Performing the division:

$7658/45$

7658 divided by 45 gives a quotient of 170 and a remainder of 8, since:

$45\times 170=7650$

Now, we can find the two numbers closest to 7658 that are divisible by 45:

1. The smaller number divisible by 45 is obtained by subtracting the remainder from 7658:
$7658-8=7650$

2. The larger number divisible by 45 is obtained by adding $(45-8)$ to 7658:
$7658+37=7695$

Comparing the distances from 7658:
Distance to 7650 = 8
Distance to 7695 = 37

Since 8 is smaller than 37, the number nearest to 7658 that is exactly divisible by 45 is 7650.