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Haryana Police Constable Model Paper 9

Question : 25 of 100

Marks: +1, -0

The remainder when 4 power 16 is divided by 5 is

Solution:

To find the remainder when a number (having some power) is divisible by any other number, find the cyclicity of that number

Cyclicity = Value of power after which the unit digit start repeating itself

Calculation:

4^{16} = (5 - 1)^{16}

On dividing it by 5,

\frac{(5 - 1)^{16}}{5} = \frac{(-1)^{16}}{5}

(∵ any power to 5 will always be divisible by 5)

∴ Remainder =

\frac{1^{16}}{5} = 1

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