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 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
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 
Step1:: Divide the power of 2 by 4. It means, divide 33 by 4.
Step2: You get remainder 1.
Step3: Since you have got 1 as a remainder , put it as a power of 2 i.e (2)^{1}.
Step4: Have a look on table, (2)^{1}=2. So, Answer will be 2
(2) Find the Unit Digit in (2)^{40}
Sol 
Step1:: Divide the power of 2 by 4. It means, divide 40 by 4.
Step2: It's completely divisible by 4. It means, the remainder is 0.
Step3: Since you have got nothing as a remainder , put 4 as a power of 2 i.e (2)^{4}.
Step4: Have a look on table, (2)^{4}=6. So, Answer will be 6
Finding the Unit Digit of Powers of 3 (same approach)
Power  Unit Digit 
(3)^{1}  3 
(3)^{2}  9 
(3)^{3}  7 
(3)^{4}  1 
Let's solve few Examples to make things clear.
(1) Find the Units Digit in (3)^{33}
Sol 
Step1:: Divide the power of 3 by 4. It means, divide 33 by 4.
Step2: You get remainder 1.
Step3: Since you have got 1 as a remainder , put it as a power of 3 i.e (3)^{1}.
Step4: Have a look on table, (3)^{1}=3. So, Answer will be 3
(2) Find the Unit Digit in (3)^{32}
Sol 
Step1:: Divide the power of 3 by 4. It means, divide 32 by 4.
Step2: It's completely divisible by 4. It means, the remainder is 0.
Step3: Since you have got nothing as a remainder , put 4 as a power of 3 i.e (3)^{4}.
Step4: 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.
For Example 
Finding the Unit Digit of Powers of 7 (same approach)
Power  Unit Digit 
(7)^{1}  7 
(7)^{2}  9 
(7)^{3}  3 
(7)^{4}  1 
Let's solve few Examples to make things clear.
(1) Find the Units Digit in (7)^{34}
Sol 
Step1:: Divide the power of 7 by 4. It means, divide 34 by 4.
Step2: You get remainder 2.
Step3: Since you have got 2 as a remainder , put it as a power of 7 i.e (7)^{2}.
Step4: Have a look on table, (7)^{2}=9. So, Answer will be 9
(2) Find the Unit Digit in (7)^{84}
Sol 
Step1:: Divide the power of 7 by 4. It means, divide 84 by 4.
Step2: It's completely divisible by 4. It means, the remainder is 0.
Step3: Since you have got nothing as a remainder , put 4 as a power of 7 i.e (7)^{4}.
Step4: Have a look on table, (7)^{4}=1. So, Answer will be 1
Finding the Unit Digit of Powers of 8 (same approach)
Power  Unit Digit 
(8)^{1}  8 
(8)^{2}  4 
(8)^{3}  2 
(8)^{4}  6 
Let's solve few Examples to make things clear.
(1) Find the Units Digit in (8)^{34}
Sol 
Step1:: Divide the power of 8 by 4. It means, divide 34 by 4.
Step2: You get remainder 2.
Step3: Since you have got 2 as a remainder , put it as a power of 8 i.e (8)^{2}.
Step4: Have a look on table, (8)^{2}=4. So, Answer will be 4
(2) Find the Unit Digit in (8)^{32}
Sol 
Step1:: Divide the power of 8 by 4. It means, divide 32 by 4.
Step2: It's completely divisible by 4. It means, the remainder is 0.
Step3: Since you have got nothing as a remainder , put 4 as a power of 8 i.e (8)^{4}.
Step4: 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 35= 2 which is negative which is not possible.
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