Easy Tips and Tricks to Find Unit Digit, Study Notes, Material - CTET Paper 1 & 2

By Ashish|Updated : May 7th, 2021

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 give 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)which always give 6 as the remainder
Easy Way to Find Unit Digit of Powers
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 (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)which always give 1 as the remainder
Easy Way to Find Unit Digit of Powers
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, 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 3 i.e (3)1.
Step-4: Have a look on the 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, 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

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)which always give 1 as the remainder
Easy Way to Find Unit Digit of Powers
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, divides 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 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 on 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)which always give 6 as the remainder
Easy Way to Find Unit Digit of Powers
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, divides 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 the 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 the table, (8)4=1. So, Answer will be 6
 
 

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

Suggested Read Books:

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

Thanks!

Sahi Prep hai toh Life Set hai!

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AshishAshishMember since Nov 2015
Ashish is a management professional with more than 4 years of experience as Mentor in Education sector. Currently working as Community Manager of Teaching exams category at Gradeup. He helps to provide quality content and solves the doubt of aspirants preparing for the exams. His email address is [email protected]
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Shikha Dubey

Shikha DubeyFeb 26, 2021

Could you please solve second ques.
Gayatri Mishra
Sir aaise hi sari digit me hoga
Ram Narine

Ram NarineFeb 26, 2021

Sir 10class results kab
Siddu Varelu
Tq sir . actually I'm poor student in maths subject.your explaination is nice sir . easy ly ican understand your explanation method .tq sir plz explain other top
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Sunakar Mandla
What kind of methods should I follow to get Teacher job.pls help me

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