For example, one cannot (without some tricks) achieve 1 μs resolution and a 1 sec maximum period using a 16-bit timer.
However the prescaler allows tweaking the ratio between resolution and maximum period to achieve a desired effect.
For this reason, it is common to either restrict the integer to a low value, or use a dual-modulus prescaler in this application.
A dual-modulus prescaler is one that has the ability to selectively divide the input frequency by one of two (normally consecutive) integers, such as 32 and 33.
Common fixed-integer microwave prescalers are available in modulus 2, 4, 8, 5 and 10, and can operate at frequencies in excess of 10 GHz.