Find the highest power of 16 contained in 125!
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Answer:
we will start by understanding an importabt concept called greatest intetger fraction
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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!.
[tex]\frac{125}{2} + \frac{125}{4} +\frac{125}{16} +\frac{125}{32} +\frac{125}{64}[/tex]
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.