Tips and Tricks to Find Unit Digit

Short Tricks To Find Unit Digit of Powers which will not only make these questions easy but will also save your time. The tricks can be used in Simplification, Approximation and other mathematics questions too. We hope the post will be helpful for the upcoming SSC CGL 2016

Important Short Tricks To Find Unit Digit of Powers

Some previous year questions asked in SSC Exams are listed below:

(a) Find the Units Place in  (567)⁹⁸ + (258)³³ + (678)⁶⁷

(b) What will come in Units Place in  (657)⁸⁵ –  (158)³⁷

These questions can be time consuming for those students who are unaware of the fact that there are shortcut methods for solving such questions.

Finding the Unit Digit of Powers of 2

1. First of all, divide the Power of 2 by 4.
2. If you get any remainder, put it as the power of 2 and get the result using the below given table.
3. If you don’t get any remainder after dividing the power of 2 by 4, your answer will be (2)⁴ which always give 6 as the remainder

Let’s solve few Examples to make things clear.(1) Find the Units Digit in (2)³³
Sol –
Step-1:: Divide the power of 2 by 4. It means, divide 33 by 4.
Step-2: You get remainder 1.
Step-3: Since you have got 1 as a  remainder , put it as a power of 2 i.e (2)¹.
Step-4: Have a look on table, (2)¹=2. So, Answer will be 2

(2) Find the Unit Digit in (2)⁴⁰
Sol –
Step-1:: Divide the power of 2 by 4. It means, divide 40 by 4.
Step-2: It’s completely divisible by 4. It means, the remainder is 0.
Step-3: Since you have got nothing as a  remainder , put 4 as a power of 2 i.e (2)⁴.
Step-4: Have a look on table, (2)⁴=6. So, Answer will be 6

Finding the Unit Digit of Powers of 3 (same approach)

1. First of all, divide the Power of 3 by 4.
2. If you get any remainder, put it as the power of 3 and get the result using the below given table.
3. If you don’t get any remainder after dividing the power of 3 by 4, your answer will be (3)⁴ which always give 1 as the remainder

Let’s solve few Examples to make things clear.(1) Find the Units Digit in (3)³³
Sol –
Step-1:: Divide the power of 3 by 4. It means, divide 33 by 4.
Step-2: You get remainder 1.
Step-3: Since you have got 1 as a  remainder , put it as a power of 3 i.e (3)¹.
Step-4: Have a look on table, (3)¹=3. So, Answer will be 3

(2) Find the Unit Digit in (3)³²
Sol –
Step-1:: Divide the power of 3 by 4. It means, divide 32 by 4.
Step-2: It’s completely divisible by 4. It means, the remainder is 0.
Step-3: Since you have got nothing as a  remainder , put 4 as a power of 3 i.e (3)⁴.
Step-4: Have a look on table, (3)⁴=1. So, Answer will be 1

Finding the Unit Digit of Powers of 0,1,5,6

 

The unit digit of 0,1,5,6 always remains same i.e 0,1,5,6 respectively for every power.

Finding the Unit Digit of Powers of 4 & 9

 

In case of  4 & 9, if powers are Even, the result will be 6 & 4. However, when their powers are Odd, the result will be 1 & 9. The same is depicted below.

• If the Power of 4 is Even, the result will be 6
• If the Power of 4 is Odd, the result will be 4
• If the Power of 9 is Even, the result will be  1
• If the Power of 9 is Odd, the result will be 9.

For Example – 

• (9)⁸⁴ = 1
• (9)²¹ = 9
• (4)⁶⁴ = 6
• (4)⁶³ = 4

Finding the Unit Digit of Powers of 7 (same approach)

1. First of all, divide the Power of 7 by 4.
2. If you get any remainder, put it as the power of 7 and get the result using the below given table.
3. If you don’t get any remainder after dividing the power of 7 by 4, your answer will be (7)⁴ which always give 1 as the remainder

Let’s solve few Examples to make things clear.
(1) Find the Units Digit in (7)³⁴
Sol –
Step-1:: Divide the power of 7 by 4. It means, divide 34 by 4.
Step-2: You get remainder 2.
Step-3: Since you have got 2 as a  remainder , put it as a power of 7 i.e (7)².
Step-4: Have a look on table, (7)²=9. So, Answer will be 9

(2) Find the Unit Digit in (7)⁸⁴
Sol –
Step-1:: Divide the power of 7 by 4. It means, divide 84 by 4.
Step-2: It’s completely divisible by 4. It means, the remainder is 0.
Step-3: Since you have got nothing as a  remainder , put 4 as a power of 7 i.e (7)⁴.
Step-4: Have a look on table, (7)⁴=1. So, Answer will be 1

Finding the Unit Digit of Powers of 8 (same approach)

1. First of all, divide the Power of 8 by 4.
2. If you get any remainder, put it as the power of 8 and get the result using the below given table.
3. If you don’t get any remainder after dividing the power of 8 by 4, your answer will be (8)⁴ which always give 6 as the remainder

Let’s solve few Examples to make things clear.(1) Find the Units Digit in (8)³⁴
Sol –
Step-1:: Divide the power of 8 by 4. It means, divide 34 by 4.
Step-2: You get remainder 2.
Step-3: Since you have got 2 as a  remainder , put it as a power of 8 i.e (8)².
Step-4: Have a look on table, (8)²=4. So, Answer will be 4

(2) Find the Unit Digit in (8)³²
Sol –
Step-1:: Divide the power of 8 by 4. It means, divide 32 by 4.
Step-2: It’s completely divisible by 4. It means, the remainder is 0.
Step-3: Since you have got nothing as a  remainder , put 4 as a power of 8 i.e (8)⁴.
Step-4: Have a look on table, (8)⁴=1. So, Answer will be 6