When calculating the sample variance, why do we divide by "n-1" and not "n-2" or "n-0.5"?

Question

When calculating the sample variance we divide by $n-1$ instead of $n$ to correct the bias that results in from using the sample mean instead of the population mean.

My question is why do we only subtract 1 and not any other value? and why don't we divide by $n-2$ for example?

Thanks for your help.