Thursday, September 10, 2015

Shortcut Trick for Finding the Units Digits of Large Powers

Easy Way of finding the Units Digit of Large Powers | How to find the Units Digit of Large Powers| Trick to find the Unit Digits of Large Powers.

In SSC CGL Exam, you may find few questions based on finding the Units Digits of Large Powers. A typical example of such questions is listed below:

(a) Find the Units Place in  (785)98 + (342)33 + (986)67

(b) What will come in Units Place in  (983)85 -  (235)37

These questions can be time consuming for those students who are unaware of the fact that there is a shortcut method for solving such questions. Don't worry if you don't know the shortcut already because we are providing it today.

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
Power Unit Digit
(2)1 2
(2)2 4
(2)3 8
(2)4 6

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)which always give 1 as the remainder
PowerUnit Digit
(3)13
(3)29
(3)37
(3)41

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)which always give 1 as the remainder
PowerUnit Digit
(7)17
(7)29
(7)33
(7)41

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)which always give 6 as the remainder
PowerUnit Digit
(8)18
(8)24
(8)32
(8)46

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


Now, you can easily solve questions based on finding the Unit's Digit of large powers. Lets try at least a few.

(a) Find the Units Place in  (785)98 + (342)33 + (986)67

Sol : 5 + 2 + 6 = 13 . So answer will be 3 .


(a) Find the Units Place in  (983)85 -  (235)37

Sol :  3 - 5 = 13 - 5 = 8  . So answer will be 8 . In this question, we have considered 3 as 13 because 3-5= -2 which is negative which is not possible.


If you have any Doubt, feel free to ask via commenting. 

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