baker

via baker we get the interesting fact that
the number of numbers less than n divisible by prime p is given by [n/p], where [] is the floor function.
since p is prime, only members of the progression {k.p} are divisible by p, and there are [n/p] of these, since p goes into n n/p times, and we can ignore the fractional part. for example, 3 goes into 10 ten thirds times, but this means that 3 numbers (3, 6, 9) less than ten are divisible by three.

this can be extended to [n/ p^2] which is the number divisible by p squared, and so on.

This tells us that the p-component of n factorial, let's call it l, is the sum over j of [n / p to the j] over all j.

this leads to a proof thatthe binomial coefficient is an integer....