Unit Digit!

Number Theory Level 1

Find the units digit of 201 4 2014 2014^{2014} .


The answer is 6.

Shubham Gantayat by Shubham Gantayat , 22, India

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3 solutions

Rohit Singh
Jun 13, 2014

You will have to see a pattern ...2014*2014= last digit 6 after that Again last digit is 4

Re

The pattern is 4,6,4,6

It repeats again after 2so 2014= 1007. And pattern reached to even no division so and is 6

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Sunil Pradhan
Jul 19, 2014

2014 (index) ÷ 4 remainder is 2

so unit digit = 2014 (base)^4 i.e. 4^2 unit digit is 6

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Ayushi Saini
Jul 7, 2014

yeah...that's the pattern...4 x 4 = 16....6 will always be the unit digit

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