If you were going to use the GPS signal as a clock input to the microcontroller, then no, you probably would not have to divide it externally if it were already of a suitable frequency. For example, your normally 16 MHz micro will probably run fine on 10 MHz, though you'll have to re-calculate divisors for any fixed-clock communication schemes.
But that's not normally how frequency counters work.
Typically, what happens is that a reference clock is divided down to produce a gating or measurement interval that is the reciprocal of the desired measurement resolution; for example, if you want 1 Hz resolution you must measure for one second. Then, during that period you count cycles of the signal being measured, either clocking from it or by sampling it with something clocked much faster.
If you want to try using the GPS reference as a microcontroller clock, then you can divide it down using a counter/timer inside your micro to produce your gating interval. But beware that your micro may not function if the GPS clock is missing - some chips would allow you to start up with an internal oscillator and switch over if the GPS clock is found, and with substantially more effort, possible switch back if it is lost - that could let you provide a meaningful error message.
It's worth noting that some microcontroller timer/counter blocks can be clocked by external signals as fast or faster than the micro's current clock input, while others must re-sample inputs with their own clock, and so cannot count inputs (either signal under test or reference) which are not a few times slower than the micro's clock).
The most flexible design would probably be one with its own crystal oscillator, and the GPS as an optional input, useful when available, but not mandatory for approximate measurements when not.
0 to 124999 is exactly 125000 counts. Starting at zero is a simple convention that can make some code a bit simpler (like working with lists and pointers), but it means that you increment to one less than the number of iterations you need.
Generally when you build a divider like this, you are interested in the half period so you can invert once every half period and get a waveform with a perfect 50% duty cycle.
Best Answer
If you want to treat this signal as a periodic one, then you can take its Fourier series.
Unlike most other periodic signals, you have free choice of what frequency to consider as its fundamental frequency --- you can calculate the series for any fundamental frequency
But regardless of which fundamental frequency you choose, you'll find that all the terms in the series except for the 0-frequency one have zero magnitude.