X
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30


 

 
1

4

9

16

25

36

49

64

81

100

121

144

169

196

225

256

289

324

361

400

441

484

529

576

625

676

729

784

841

900


 


1

8

27

64

125

216

343

512

729

1000

1331

1728

2197

2744

3375

4096

4913

5832

6859

8000

9261

10648

12167

13824

15625

17576

19683

21952

24389

27000

 

 

Finding the unit digit of given numbers:

Now let us observe the pattern in the cycle of different digit in other words after how many cycles the last digit repeats itself.
 

  2

3

4

5

6

7

8

9

 2= 2

 3= 3

  4= 4

  5= 5

   6= 6

 7= 7

 8= 8

 9= 9

 2= 4

 3= 9

  4= 6

 5= 5 

 6= 6

 7= 9

 8= 4

  9= 1

  2= 8

  3= 7

  4= 4

  5= 5

  6= 6

  7= 3

  8= 2

  9= 9 

 2= 6

  3= 1

   4= 6

   5= 5

  6= 6

   7= 1

  8= 6

   9= 1

  2= 2

  3= 3

   4= 4

   5= 5

  6= 6

    7=  7

  8= 8

 9= 9

  2= 4 

 3= 9

  4=6 

  5= 5

  66 = 6

  7= 9

  8= 4

  9= 1

  2= 8

  3= 7

  4= 4

  57= 5

  6=  6

   7= 3

  8= 8

   9= 9

from the above table we can conclude that

after each power that is either 4 or multiple of four the digits repeats themselves
 

Q 1) find the unit digit of 257

We know in case of 2, it repeats itself after a cycle of 4 . We will divide 57 by 4

57/4 remainder is 1

We write it as

257= 21= 2

That means the unit digit in the 257 is 2.


 

Q 2) find the unit digit of 388 ?

Solution:

88/4 the remainder is 0.

In such cases, our answer should be the 4th power

So answer is unit digit in 34is 1.



Q3)  find the unit digit of 7458000

Solution: In this case we need to divide the power by 4

The power is 458000

or 458000/4 = 0 remainder
74if you still find difficult, let us simplify it

74= 7× 72

= 9 × 9 (Unit digits)

81 Unit digit so the last digit in the 7458000is

 

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