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Question Number 19499 by tawa tawa last updated on 12/Aug/17

$$\mathrm{Find}\mathrm{the}\mathrm{last}\mathrm{digit}\mathrm{of}{2}^{253}$$

Answered by Tinkutara last updated on 12/Aug/17

$$\mathrm{Cyclicity}\mathrm{of}2=4(2,4,8,6)$$$$253\equiv 1\left(\mathrm{mod}4\right)$$$$\therefore 2^{253}\equiv 2^1\equiv 2$$$$\mathrm{Last}\mathrm{digit}=2$$

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