What is the last (units) digit of 333^444 ?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Any number which has a units digit of 1, will continue to have the same digit no matter what is the power it is raised to.

We can write 333^444 as (333^4)^111.

Any number which has a units digit of 3 when raised to the power 4 has a units digit of 1.

This make 333^4 a number with a units digit of 1.

Therefore 333^4 raised to any power will continue to have a units digit of 1.

So the required units digit of 333^444 is 1.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To determine the last digit  number in unit place of 333^444

We know that  the last digitof 333^4 = is e as the same as the last digit of 3^4 = last digit in 81. So it is 1.

Therefore the last digit of 333^444 is the same as last digit of (333^4)^111 which is 1.

=> The last digit of of 333^444  is the same as the last digit of 81^111.

But the last digit 81^n, for any positive integer n

So the last digit of 333^444 is 1.

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