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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**

- 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

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)**

- 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 give 1 as the remainder

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 -

**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)**

- 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

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 -

**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)**

- 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

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 -

**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.

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