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.
Hello, Ideasman
How do I determine what the highest power of 2 is that divides 89,275,744?
Convert $\displaystyle 89,275,744$ to binary and we get:
. . $\displaystyle 101,010,100,100,011,110,101,100,000_2$
. . . . . . . . . . . . . . . . . . . - - - $\displaystyle \uparrow$
. . . and it is obvious that $\displaystyle \overbrace{100000_2 = 32}$ is the greatest divisor.
Just kidding!