NUMBER SYSTEM II

Finding Digit?

Finding Last Digit(Units Digit) of X^n , Where x is an integer and n is a positive integer

Example - 12*12 = LD(4)

                  2^3 = 8

                  LD(12^3) = __8

• The last digit of X^n depends only on the last digit of x itself raised to the power.

• Last Digits of the powers of any digit follow a cyclic pattern i.e. they repeat after a certain number of steps.

• If the last digit of the base x is 0 or 1 or 5 or 6 then the last digit of the result when x is raised to a positive power integer power is 0,1,5 and 6 respectively.

• If the last of the base x is 4 or 9 then 

             For 4, every odd power will give the last digit of 4 and every even power will give last digit 6

             For 9, every odd power will give the last digit of 9 and every even power will give last digit 1

• If the last digit of base x is 2 or 3 or 7 or 8 then divide the power by 4 and replace it by the remainder obtained and use that to obtain the last digit if the remainder is 0 take it as 4  (apply divisibility rule for simplicity )

Finding Last Two Digits ( Tens and Unit Digit) of x^n, Where x is an integer and n is a positive integer

Criss-Cross Multiplication