**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 result using the below-given table.
- 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

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**

**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)**

- 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 result using the below-given table.
- 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 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)**

- 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 result using the below-given table.
- 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 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.

**Suggested Read Books:**

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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