Question

Find the highest power of 16 contained in 125!

Answer 1

Answer:

we will start by understanding an importabt concept called greatest intetger fraction

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Answer 2

Answer:

The correct answer of this question is  119.

Step-by-step explanation:

Given -  The highest power of 16 contained in 125 .

To Find - Find the highest power of 16 contained in 125 .

According to the question -

The highest powers of 16 in 125! are 119

So, 16 is not a prime number

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!.

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

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.