# Easy Tips and Tricks to Find Unit Digit, Study Notes, Material

By Ashish Kumar|Updated : August 9th, 2022

## 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

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)which always gives 6 as the remainder.
Finding the Unit Digit of Powers of 4 & 9

In the 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

## 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

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)4which always give 6 as the remainder

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, dividing 33 by 4.
Step-2: You get the 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, the answers will be 2

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

• 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 result using the below-given table.
• If you don't get any remainder after dividing the power of 3 by 4, your answer will be (3)4 which always gives 1 as the remainder

Let's solve a 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, dividing 33 by 4.
Step-2: You get the 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 at the table, (3)1=3. So, the answers will be 3

(2) Find the Unit Digit in (3)32
Sol -
Step-1: Divide the power of 3 by 4. It means, dividing 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 at the 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 the 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)4which always give 1 as the remainder

Let's solve a 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, dividing 34 by 4.
Step-2:You get the 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 at the 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, divides 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 at the 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)4which always give 6 as the remainder

Let's solve a 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, dividing 34 by 4.
Step-2: You get the 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 at the table, (8)2=4. So, answers will be 4

(2) Find the Unit Digit in (8)32
Sol-
Step-1:Divide the power of 8 by 4. It means, dividing 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 at the table, (8)4=1. So, answers will be 6

This article tends to be beneficial for the following exams -REET, UPTET, CTET, Online Classroom Program TET, DSSSB, KVS etc.

 Serial No. Book Name Author Name 1. Quantitative Aptitude for Competitive Examinations, Edition 7 R S Aggarwal 2. Mathematics Exam Goalpost for CTET & TETs Wiley Publication

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## FAQs

• Sol -

Step-1:: Divide the power of 3 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 3 i.e (3)4.

Step-4: Have a look on the table, (3)4=1. So, Answer will be 1

• 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

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

• Now, divide the power, i.e. 105 by 4. 105/4 gives the quotient 26 and remainder 1. So, the required unit digit will be the unit digit of 71. This will be 7.

• Hence, the unit digit of 3 to the power 34 will be 9

•

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 the 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.

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