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Number Theory Level 2

What is the last digit of $2^{10^{9}}$ ? For example, the last digit of $2^{5}$ = $2$ .

The answer is 6.

2 solutions

Kay Xspre
Oct 11, 2015

The last digit of $2^x$ when $x$ is a positive integer will be in the sequence of $2, 4, 8, 6, 2, 4, 8, 6, \dots$ , a relation with period of 4, so you will need to find the reminder of $\frac{10^9}{4}$ . The reminder is 0, thus the last digit will end with 6.

Same method. Didn't even require a pen and paper for me. Just a mental calculation.

Satyajit Ghosh - 5 years, 7 months ago

Sadasiva Panicker
Oct 22, 2015

last digit of 2^10 = 4, last digit of 2^100 =6, 2^1000=6, in thi way 2^1000000000 =6: ie 2^10^9 end in 6

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The answer is 6.

2 solutions

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