A number theory problem by Kamala Ramakrishnan

Number Theory Level 1

What is the units digit of 2 30567 ? 2^{30567}?


The answer is 8.

Kamala Ramakrishnan by Kamala Ramakrishnan , 50, India

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3 solutions

The pattern followed for the unit's digits are 2-4-8-6-2-4-8-6...

Thus, every power divisible by 4 has the unit's digit as 6.

30564 is divisible by 4. Hence the unit's digit of 30567 is 8.

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Rama Devi
May 26, 2015

The given exponent is in the form 2^4n+3 , whose last digit is 8.Therefore the solution of this is also 8.

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Ely Gangat
Jul 18, 2014

the cycle for the units digit for base 2 is 2,4,8,6.

if exponent(mod 4)=1 then the 1st of the cycle is the units digit.

if exponent(mod 4)=2 then the 2nd of the cycle is the units digit.

if exponent(mod 4)=3 then the 3rd of the cycle is the units digit.

if exponent(mod 4)=0 then the 4th of the cycle is the units digit.

30567(mod4) = 3

therefore the 3rd of the cycle, 8, is the units digit.

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