How to Find Unit Digit of a Power Number | Unit Digit Problems with Solutions

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Finding the Last Digit of any Number With Power | Unit place of a Number

In Quantitative aptitude, questions asked to find the last digit and last two digits of a power or large expression. This article explained different types of tools to serve as shortcuts to finding the last digits of an expanded power.

Find the last digit of a number with power

First, identify the pattern last digit (unit place) for the power of numbers “N”

Digit N¹	N²	N³	N⁴	N⁵	N⁶	N⁷	N⁸	N⁹
1	1	1	1	1	1	1	1	1
2	4	8	6	2	4	8	6	2
3	9	7	1	3	9	7	1	3
4	6	4	6	4	6	4	6	4
5	5	5	5	5	5	5	5	5
6	6	6	6	6	6	6	6	6
7	9	3	1	7	9	3	1	7
8	4	2	6	8	4	2	6	8
9	1	9	1	9	1	9	1	9

From the above table, we can observe as following

The last digit of power of 1, 5 & 6 is always comes same number as a unit place.

The last digit of power of 2 repeats in a cycle of numbers – 4, 8, 6 & 2

The last digit of power of 3 repeats in a cycle of numbers – 9, 7, 1 & 3

The last digit of power of 4 repeats in a cycle of numbers – 6 & 4

The last digit of the power of 7 repeats in a cycle of numbers – 9, 3, 1, & 7

The last digit of the power of 8 repeats in a cycle of numbers – 4, 2, 6 & 8

The last digit of the power of 9 repeats in a cycle of numbers – 1 & 9

Explanation:

If the Last digit ( Unit place ) of numbers having 1 , 5 & 6

- ( – – – – 1)ⁿ = ( – – – – 1)
- (- – – – -5)ⁿ = ( – – – – 5)
- (- – – – -6)ⁿ = (- – – – -6)

If the unit place ( Last digit ) of any number “ Aⁿ” having 2, 3, 7 or 8, then the unit place of that number depends upon the value of power “ n” and follows

Expressed power “ n”	Unit Place of ( – – -2)ⁿ	Unit Place of ( – – -3)ⁿ	Unit Place of ( – – -7)ⁿ	Unit Place of ( – – -8)ⁿ
4x	6	1	1	6
4x + 1	2	3	7	8
4x + 2	4	9	9	4
4x + 3	8	7	3	2

If the unit place ( Last digit ) of any number “ Aⁿ” having 4 & 9 then the unit place of that number depends upon the value of power “ n” and follows

Expressed power “ n”	Unit Place of ( – – -4)ⁿ	Unit Place of ( – – -9)ⁿ
2x (Even number)	6	1
2x + 1 (Odd number)	4	9

Last digit of a number of questions

Examples – 1 : Find the last digit of the number 3²⁰¹⁵

Solution: The power 2015 can be written as [ (503 x 4) + 3 ]

So from the above table unit digit of a given number is – 7

Examples – 2: Find the last digit of the number 4444²⁰¹⁵

Solution: Here power value is an odd number

So the last digit of the given number is 4

Hint: The last digit of any number having “4” then power has an even number then unit place becomes 6 and power has an odd number then unit place becomes 4

Example 3 : What is the last digit of the number 4²⁰¹²

Solution: Here power value is an even number. So unit digit of the given number is 6

Examples – 4 : Find the last digit of the number 11¹²³⁺⁵

Solution: Here The unit place has ” 1″ so the final number also comes ” 1″ as a unit place

Examples – 5 : Find the digit at the unit place of the number 19²⁵

Hint: The last digit of any number having “9” then power has an even number then unit place becomes 1 and power has an odd number then unit place becomes 9

Solution: Here power has an odd number so the final number unit place comes ” 9″

Examples – 6: Find the digit at the unit place of the number $3^{(99-3)^{50}}$