**General Rule to find the unit place digit**

**Example: (23 x 45 x 37 x 345 x 5659) = ……?**

Setp1. We collect the first digit of every number.

3, 5, 7, 5, 9

Step2. Multiply first two digits: 3 x 5 = 15

Step3. Unit place digit of 15 is 5.

Step4. 5 is multiply with 7: 5 x 7 = 35

Step5. Unit place digit of 35 is 5.

Step6. 5 is multiply with 5: 5 x 5 = 25.

Step7. Unit place digit of 25 is 5.

Step8. 5 is multiply with 9: 5 x 9 = 45

Hence, the unit place digit of the number is 5.

**How to find the unit place digit of (…..2)**^{n}.

^{n}.

(..2)^{1} = 2. The unit place digit is 2.

(..2)^{2} = 4. The unit place digit is 4.

(..2)^{3} = 8. The unit place digit is 8.

(..2)^{4} = 16. The unit place digit is 6.

(..2)^{5} = 32. The unit place digit is 2.

(..2)^{6} = 64. The unit place digit is 4.

(..2)^{7} = 128. The unit place digit is 8.

(..2)^{8} = 256. The unit place digit is 6.

It repeats the process in multiple of 4.

Hence, To make it in the power of (…2)^{4n or 4n+1,2,3}

**How to solve it easily?**

First check the divisibility of power with 4.

If the reminder is 0, The unit place digit will be 6.

If the reminder is 1, The unit place digit will be 2.

If the reminder is 2, The unit place digit will be 4.

If the reminder is 3, The unit place digit will be 8.

**Example 1: (36572) ^{48} = (….?)**

Lets make the power in the multiple of 4n

(36572)^{4×12} = (….6)

**Example 2: (36572) ^{49} = (….?)**

Lets make the power in the multiple of 4n+1

(36572)^{4×12+1} = (….2)

**Example 3: (36572) ^{50} = (….?)**

Lets make the power in the multiple of 4n+2

(36572)^{4×12+2} = (….4)

**Example 4: (36572) ^{51} = (….?)**

Lets make the power in the multiple of 4n+3

(36572)^{4×12+3} = (….8)

**Find the unit place digit?**

(46572)^{234} |

(579382)^{465} |

(756852)^{547} |

(57862)^{768} |

(734792)^{8797} |

(8976452)^{4354} |

(358732)^{86869} |

(67492)^{544774} |

(896802)^{78585} |

(73534892)^{65757} |

**How to find the unit place digit of (…..3)**^{n}.

^{n}.

(..3)^{1} = 3. The unit place digit is 3.

(..3)^{2} = 9. The unit place digit is 9.

(..3)^{3} = 27. The unit place digit is 7.

(..3)^{4} = 81. The unit place digit is 1.

(..3)^{5} = 243. The unit place digit is 3.

(..3)^{6} = 729. The unit place digit is 9.

(..3)^{7} = 2187. The unit place digit is 7.

(..3)^{8} = 6561. The unit place digit is 1.

It repeats the process in multiple of 4.

Hence, To make it in the power of (…3)^{4n or 4n+1,2,3}

**How to solve it easily?**

First check the divisibility of power with 4.

If the reminder is 0, The unit place digit will be 1.

If the reminder is 1, The unit place digit will be 3.

If the reminder is 2, The unit place digit will be 9.

If the reminder is 3, The unit place digit will be 7.

**Example 1: (36573) ^{48} = (….?)**

Lets make the power in the multiple of 4n

(36573)^{4×12} = (….1)

**Example 2: (36573) ^{49} = (….?)**

Lets make the power in the multiple of 4n+1

(36573)^{4×12+1} = (….3)

**Example 3: (36573) ^{50} = (….?)**

Lets make the power in the multiple of 4n+2

(36573)^{4×12+2} = (….9)

**Example 4: (36573) ^{51} = (….?)**

Lets make the power in the multiple of 4n+3

(36573)^{4×12+3} = (….7)

**Find the unit place digit?**

(46573)^{234} |

(579383)^{465} |

(756853)^{547} |

(57863)^{768} |

(734793)^{8797} |

(8976453)^{4354} |

(35873)^{86869} |

(67493)^{544774} |

(896803)^{78585} |

(7353483)^{65757} |

**How to find the unit place digit of (…..4)**^{n}.

^{n}.

If the power is odd number.

The unit place digit will be 4.

If the power is even number.

The unit place digit will be 6.

**Find the unit place digit?**

(46574)^{234} |

(579384)^{465} |

(756854)^{547} |

(57864)^{768} |

(734794)^{8797} |

(8976454)^{4354} |

(35874)^{86869} |

(67494)^{544774} |

(896804)^{78585} |

(7353484)^{65757} |

**How to find the unit place digit of (…..9)**^{n}.

^{n}.

If the power is odd number.

The unit place digit will be 9.

If the power is even number.

The unit place digit will be 1.

**Find the unit place digit?**

(46579)^{234} |

(579389)^{465} |

(756859)^{547} |

(57869)^{768} |

(734799)^{8797} |

(8976459)^{4354} |

(35879)^{86869} |

(67499)^{544774} |

(896809)^{78585} |

(735349)^{65757} |

**How to find the unit place digit of (…..7)**^{n}.

^{n}.

(..7)^{1} =7. The unit place digit is 7.

(..7)^{2} = 49. The unit place digit is 9.

(..7)^{3} = 343. The unit place digit is 3.

(..7)^{4} = 2401. The unit place digit is 1.

(..7)^{5} = 16807. The unit place digit is 7.

(..7)^{6} = 117649. The unit place digit is 9.

(..7)^{7} = 823543. The unit place digit is 3.

(..7)^{8} = 5764801. The unit place digit is 1.

It repeats the process in multiple of 4.

Hence, To make it in the power of (…7)^{4n or 4n+1,2,3}

**How to solve it easily?**

First check the divisibility of power with 4.

If the reminder is 0, The unit place digit will be 1.

If the reminder is 1, The unit place digit will be 7.

If the reminder is 2, The unit place digit will be 9.

If the reminder is 3, The unit place digit will be 3.

**Example 1: (36577) ^{48} = (….?)**

Lets make the power in the multiple of 4n

(3657)^{4×12} = (….1)

**Example 2: (3657) ^{49} = (….?)**

Lets make the power in the multiple of 4n+1

(3657)^{4×12+1} = (….7)

**Example 3: (3657) ^{50} = (….?)**

Lets make the power in the multiple of 4n+2

(3657)^{4×12+2} = (….9)

**Example 4: (3657) ^{51} = (….?)**

Lets make the power in the multiple of 4n+3

(3657)^{4×12+3} = (….3)

**Find the unit place digit?**

(4657)^{234} |

(57937)^{465} |

(75687)^{547} |

(5787)^{768} |

(734797)^{8797} |

(8976457)^{4354} |

(3587)^{86869} |

(67497)^{544774} |

(896807)^{78585} |

(7353487)^{65757} |

**How to find the unit place of digit of (…5)**^{n} = (….5).

^{n}= (….5).

**How to find the unit place of digit of (…6)**^{n} = (….6).

^{n}= (….6).

**How to find the unit place digit of (…..8)**^{n}.

^{n}.

(..8)^{1} = 8. The unit place digit is 8.

(..8)^{2} = 64. The unit place digit is 4.

(..8)^{3} = 512. The unit place digit is 2.

(..8)^{4} = 4096. The unit place digit is 6.

(..8)^{5} = 32768. The unit place digit is 8.

(..8)^{6} = 262144. The unit place digit is 4.

(..8)^{7} = 2097152. The unit place digit is 2.

(..8)^{8} = 16777216. The unit place digit is 6.

It repeats the process in multiple of 4.

Hence, To make it in the power of (…8)^{4n or 4n+1,2,3}

**How to solve it easily?**

First check the divisibility of power with 4.

If the reminder is 0, The unit place digit will be 6.

If the reminder is 1, The unit place digit will be 8.

If the reminder is 2, The unit place digit will be 4.

If the reminder is 3, The unit place digit will be 2.

**Example 1: (36578) ^{48} = (….?)**

Lets make the power in the multiple of 4n

(36578)^{4×12} = (….6)

**Example 2: (36578) ^{49} = (….?)**

Lets make the power in the multiple of 4n+1

(36578)^{4×12+1} = (….8)

**Example 3: (36578) ^{50} = (….?)**

Lets make the power in the multiple of 4n+2

(36578)^{4×12+2} = (….4)

**Example 4: (36578) ^{51} = (….?)**

Lets make the power in the multiple of 4n+3

(36578)^{4×12+3} = (….2)

**Find the unit place digit?**

(46578)^{234} |

(57938)^{465} |

(7568)^{547} |

(578)^{768} |

(7348)^{8797} |

(89768)^{4354} |

(358738)^{86869} |

(67498)^{544774} |

(8968)^{78585} |

(735348)^{65757} |

**Q: 1043 is divisible by any number to get the Quotient = 11 and Reminder = 20. Find the divisor?**

**Solution:** First understand the question carefully.

Remind the given things: D = 1043; Q = 11 and R = 20

Reminder is excess in dividend, Subtract it.

1043 – 20 = 1023

Then,

1023/11 = 93 = Divisor **Ans.**

**Q: A number is divided by 195 to get reminder 47. If the same number is divided by 15, then, what will be the reminder?**

**Solution:** First understand the question carefully.

**In first case:** Remind the given things: Divisor = 195; R = 47.

**In second case:** Divisor = 15.

In this case, If 195 is divisible by 15,

then, divide 47 by 15 and get the reminder = 2.** Ans**

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