General results on the change of the parity of a number by repeatedly dividing by 2

Question

I know this question may seem open, but I'm a bit interested in figuring out, getting some ideas, or at least getting some sources on how the parity of a number is affected by repeatedly diving it by 2. My question specifically is

How many times can an even number $n$ be divided by 2 before reaching an odd number?

I guess this is in a way related to the Collatz Conjecture and I'm not sure if this question is ground-breaking in anyway but I did some research and could not find anything significant. I guess it could also be rephrased to given the prime decomposition of a number, how many $2$s will there be?

Answer 1

This nowhere groundbreaking: Any even number is of the form $2^md$ with $m \geq 1$ and $d$ odd. You can repeatedly divide it by $2$ precisley $m$ times.

Answer 2

All even numbers are clearly divisible by 2, i.e. divisible by 2 once.

50% of those will be divisible by 4, i.e. divisible by 2 twice.

50% of those, i.e. 25% of all even numbers, will be divisible by 8, i.e. divisible by 2 thrice.

50% of those, i.e. 12.5% of all even numbers will be divisible by 16, i.e. divisible by 2 four times.

etc...