Question

what is the highest power of 2 in 17!​

Answer 1

Highest power of 2 is 0

Step-by-step explanation:

Answer 2

The highest power of 2 in 17! is 15.

• To obtain the highest power of 2 in 17! we have to use the de polignac's formula to calculate it.

• Now it says that for any prime number p and any positive integer n, the exponent of the largest power of p that divides n is $\sum _{{i=1}}^{{\infty }}\left\lfloor {\frac {n}{p^{i}}}\right\rfloor ,$where $\lfloor x\rfloor$ is the floor function.  
• Here p=2 and n=17
• Now applying this formula we get $\sum _{{i=1}}^{{\infty }}\left\lfloor {\frac {17}{2^{i}}}\right\rfloor =$ $\lfloor \frac{17}{2^{1} } \rfloor + \lfloor \frac{17}{2^{2} } \rfloor + \lfloor \frac{17}{2^{3} } \rfloor + \lfloor \frac{17}{2^{4} } \rfloor$

• This evaluates to $\lfloor \frac{17}{2 } \rfloor + \lfloor \frac{17}{4} } \rfloor + \lfloor \frac{17}{8} } \rfloor + \lfloor \frac{17}{16} } \rfloor$
• This is equal to 8+4+2+1 = 15
• Hence the highest power of 2 in 17! is 15.