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Math Help - Divisibility Rules

  1. #1
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    Divisibility Rules

    How do I determine what the highest power of 2 is that divides 89,275,744?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Ideasman View Post
    How do I determine what the highest power of 2 is that divides 89,275,744?
    Well its less than \log_2(89275744) \approx 18.3, so repeated division untill you get a odd answer is a viable option. I make it 5.

    RonL
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  3. #3
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    Quote Originally Posted by Ideasman View Post
    How do I determine what the highest power of 2 is that divides 89,275,744?
    The theorem says, and follow the pattern....

    N is divisible by 2 if and only if the last digit is even.

    N is divisible by 4=2^2 if and only if the last two digits are divisible by 4.

    N is divisible by 8=2^3 if and only if the last three digits are divisible by 8.

    And thus on.....

    Thus, given 89,275,744

    1)We see it is divisible by 2 because 2 divides 2.

    2)We see it is divisible by 2^2 because 4 divides 44.

    3)We see it is divisible by 2^3 because 8 divides 744.

    And so on....
    Find the point where it stops being divisible and you have an answer.
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  4. #4
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    Hello, Ideasman

    How do I determine what the highest power of 2 is that divides 89,275,744?

    Convert 89,275,744 to binary and we get:

    . . 101,010,100,100,011,110,101,100,000_2
    . . . . . . . . . . . . . . . . . . . - - - \uparrow
    . . . and it is obvious that \overbrace{100000_2 = 32} is the greatest divisor.



    Just kidding!
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