What digit appears in unit place when $2^{320}$ is multiplied out  Is there a way to answer the following preferably without a calculator 


What digit appears in unit place when $2^{320}$ is multiplied out ? a)$0$ b)$2$ c)$4$ d)$6$ e)$8$
     ---- Ans(d)



As the ending digits for powers of two are
$${2}^{0} \mapsto 1$$
$${2}^{1} \mapsto 2$$
$${2}^{2} \mapsto 4$$
$${2}^{3} \mapsto8$$
$${2}^{4} \mapsto6$$
$${2}^{5} \mapsto2$$
You only have to do ${2}^{320 \mod(4)}$ to get the ending digit.
