Term for continuously halving a number

In summary, the conversation discussed the concept of repeatedly dividing a number by 2 until you reach a non-whole number, and the search for a mathematical term to describe this process. Various suggestions were made, such as "greatest odd divisor," "shift 'til you lift," "right-normalized floating point," "trim trailing zeroes," and "POP factor." However, it was ultimately concluded that there may not be a specific term for this process.
  • #1
dazza555
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TL;DR Summary
What is the mathematical term for continuously halving a number until you won't result in a whole number.
It's been a long time since I've had a need for my math knowledge and as a result, sadly, a lot has been forgotten. I had a thought the other day and it has been bugging me ever since. What is the mathematical term for when you continually divide any number by 2 until you no longer get a whole number, what is the function for this?

For example if I had 8/2=4 then 4/2=2 then 2/2=1 and the answer would be 1
or
94/2=47 the answer is 47

Am I just driving myself crazy thinking there is a term or proper way of writing it when it's just simply halving a number until you can't? Ahh the mind is a terrible thing to lose.
 
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  • #2
I don't think there's a term for it. I guess you could describe it as the greatest odd divisor of the number.
 
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  • #3
Write it in binary. Shift the bits right to remove the zero bits at the end. Stop when the rightmost bit is a 1.
 
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  • #4
Removing all the factors of two? Or finding the largest odd factor?
 
  • #5
robphy said:
Write it in binary. Shift the bits right to remove the zero bits at the end. Stop when the rightmost bit is a 1.

Oh nice, we can give this a snappy name. Shift 'til you lift (the rightmost digit from a 0 to a 1).

You just mumble the parenthetical part as fast as you can.
 
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  • #6
Right-normalized floating point?
 
  • #7
Here’s a catchy name:
trim trailing zeroes...
but maybe it’s more precise to say:
trim trailing zero-bits
 
  • #8
My suggestion: POP Factor (product (of) odd prime factors). Could even be a television show.
 

FAQ: Term for continuously halving a number

What is the term for continuously halving a number?

The term for continuously halving a number is called "iterative halving".

Is there a specific mathematical formula for iterative halving?

Yes, the formula for iterative halving is N/2x, where N is the original number and x is the number of times the number is halved.

What is the purpose of iterative halving in mathematics?

Iterative halving is often used in algorithms and problem-solving to find the logarithm of a number. It is also useful in simplifying fractions and solving geometric problems.

Can iterative halving be used on any number?

No, iterative halving is typically used on positive integers. It can also be used on decimals and fractions, but the results may not be as straightforward.

How does iterative halving relate to exponential growth and decay?

Iterative halving is closely related to exponential growth and decay because each iteration represents a division by a constant factor, which is a characteristic of exponential functions.

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