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How do I know how many times a number is divisible by 2 till you reach an odd number?

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You just do the obvious thing, which is to check if the number is odd, if not, you divide by 2 until you get an odd number. There is no known way to speed up the process.

If you think about it, this is similar to asking whether or not a polynomial has a double root. For this we have the derivative to help. Unfortunately, for integers we do not have a method to check for repeated primes.
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