FIND THE UNIT DIGIT

1)Find the unit digit of (142)⁴¹ + (613)¹⁶

A)1

B)2

C)3

D)4

2)Find the digit of (723)⁴²⁷ x (519)³¹⁵ x (436)⁶² x (613)¹⁶

A)1

B)2

C)3

D)6

3)What is the unit digit of 1⁵ + 2⁵ + 3⁵ + ………+20⁵

A)0

B)5

C)2

D)4

4)Find the unit digit of 376!

A)0

B)2

C)6

D)8

5)If the unit digit of (433 x 456 x43N) is (N+2), then what is the value of N ?

A)1

B)8

C)3

D)6

6)If the unit digit of (239 x346 x34N) is (N+6) , then what is the value of N ?

A)1

B)2

C)4

D)7

7)What is the unit digit of sum of first 121 natural numbers ?

A)1

B)2

C)3

D)4

8)If N=1+11+111+1111+……+111111111 then what is the sum of the digit’s of N ?

A)45

B)18

C)36

D)5

9)What is unit digit of 1⁶ + 2⁶ + 3⁶ + ….. + 20⁶?

A)0

B)1

C)2

D)4

10)What is the unit digit of (67)²⁵-1

A)6

B)8

C)0

D)3

Important Short Tricks To Find Unit Digit of Powers

Some previous year questions asked in CTET 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

First of all, divide the Power of 2 by 4.

If you get any remainder, put it as the power of 2 and get the unit digit

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 unit digit

Let's solve a 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, divides 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 at the table, (2)¹=2. So, Answer will be 2

Finding the Unit Digit of Powers of 3

First of all, divide the Power of 3 by 4.

If you get any remainder, put it as the power of 3 and get the unit digit

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 unit digit

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

First of all, divide the Power of 7 by 4.

If you get any remainder, put it as the power of 7 and get the unit digit

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 unit digit

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

First of all, divide the Power of 8 by 4.

If you get any remainder, put it as the power of 8 and get the unit digit

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 unit digit

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, divides 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