Concept: The last digit of any power
Last digit of any power follow a cycle pattern and repeat
after a certain power at a time.
From the above explanation it is clear that after the power
of four number of digit will be same.
So find out the last
digit we divide the power of any number by 4.
Digit (d)
|
d^2
|
d^3
|
d^4
|
d^5
|
1
|
1
|
1
|
1
|
1
|
2
|
4
|
8
|
6
|
2
|
3
|
9
|
7
|
1
|
3
|
4
|
6
|
4
|
6
|
4
|
5
|
5
|
5
|
5
|
5
|
6
|
6
|
6
|
6
|
6
|
7
|
9
|
3
|
1
|
7
|
8
|
4
|
2
|
6
|
8
|
9
|
1
|
9
|
1
|
9
|
0
|
0
|
0
|
0
|
0
|
v The last digit of power of 1 is always 1
v
The last digit of power of 2 repeat in a cycle
of 4, 8, 6, 2
v
The digits of powers of 3 repeat in a cycle of
9, 7, 1, 3
v
The last digit of power of 4 repeat in a cycle
of 6, 4
v
The last digit of power of 5 & 6 is always
same.
v
The last digit of power of 7 repeat in a cycle
of 9, 3, 1, 7.
v The last digit of power of 8 repeat in a cycle of 4, 2,6,8.
v The digits of powers of 9 repeat in a cycle of 1,9.
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