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Units Digit/ Unit Place Value

Saravana Kumar
4 hrs ago 0 0

Number

0

1

2

3

4

5

6

7

8

9

Power of 1

0

1

2

3

4

5

6

7

8

9

Power of 2

0

1

4

9

6

5

6

9

4

1

Power of 3

0

1

8

7

4

5

6

3

2

9

Power of 4

0

1

6

1

6

5

6

1

6

1

Power of 5

0

1

2

3

4

5

6

7

8

9

Cyclicity of 0, 1, 5, 6 – 1 time

Cyclicity of 4, 9 – 2 times

Cyclicity of 2, 3, 7, 8 – 4 times

 

What is the unit digit of (217)^413×(819)^547×(414)^624×(342)^812 ?

  • Power series of 7 i.e units digit 7 power expansion has 7,9,3 and 1 and it is raised to power 413 i.e 413/4 remainder 1 and so last digit is 7.
  • Power series of 9 i.e units digit 9 power expansion has 9 and 1 and it is raised to power 547 i.e 547/2 remainder 1 and so last digit is 9.
  • Power series of 4 i.e units digit 4 power expansion has 4 and 6 and it is raised to power 624 i.e 624/2 remainder 0 and so last digit is 6
  • Power series of 2 i.e units digit 2 power expansion has 2,4,8 and 6 and it is raised to power 812 i.e 812/4 remainder 0 and so last digit is 6.
  • All the last digits product=7*9*6*6 =8.

 

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