Question

The highest power of 16 in 125! ?​

Answer 1

The highest power of 16 in 125! is 119.

Step-by-step explanation:

As we know 16 isn't a prime number we will find maximum power of 2 in 125!.

As, 16 = (2)(2)(2)(2)

Maximum powers of 2 = Multiples of 2 in 125! + Multiples of 4 in 125! + Multiples of 8 in 125! + Multiples of 16 in 125! + Multiples of 32 in 125! + Multiples of 64 in 125!.

$= \frac{125}{2} + \frac{125}{4} + \frac{125}{16}+ \frac{125}{32}+ \frac{125}{64}$

We are going to consider the quotient if whole number, integer less than quotient if decimal.

= 62 + 31 + 15 + 7 + 3 + 1 = 119

Therefore, highest powers of 16 in 125! are 119.