Haryana Police Constable Model Paper 9

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:
$4^{16}={\left(5\mathit{–}1\right)}^{16}$
On dividing it by 5,
$\frac{{\left(5\mathit{–}1\right)}^{16}}{5}=\frac{{\left(-1\right)}^{16}}{5}$ (∵ any power to 5 will always be divisible by 5)
∴ Remainder = $\frac{{\left(1\right)}^{16}}{5}=1$