Question

What is the ones digit in the number 2^2054

Answer 1

The ones digit of the powers of two form a pattern:

`\begin{gathered} 2,4,8,6,2,4,8,6\ldots \\ 2^12^22^32^4,2^52^62^72^8\ldots \end{gathered}`

Notice that the ones digit form a repeating pattern such that even powers that are multiples of 4 have the ones digit 6.

Notice that the even powers that are not multiples of 4 have ones digit of 4

Since the given power 2054 is not a multiple of 4 but an even power it follows that the ones digit in the number 2^2054 is also 4.

The ones digit in the number 2^2054 is 4.