# Finding Last Two digits

There can be direct questions on finding last two digits of any power of a natural number and this is very important for eliminating options in questions. Following are the four simple cases with which we will be able to solve almost every problem.

**Rules for Finding Last Two Digits of square of a number**

In order to find the last two digits of square of any two digit number number, we can write it as difference
or sum from 50 or 100, whichever is closer.** In general the last two digits of a number (50±k) ^{2}
or (100-k)^{2} will be determined by square of k**.

*e.g* 47^{2} can be written as (50-3)^{2},

Now, the last two digits will be determined by square of 3 that is 09

**Rules for Finding Last Two Digits of any power of a number**

For a natural number N

^{k}, where N is a natural number ending with 0 and K is a natural number greater than 2,

**Last two digits will always be 00**.For a natural number N

^{k}, where N is a natural number ending with 5 and K is a natural number greater than 2,

**Last two digits will always be 25**.For a natural number (2×m)

^{40k+1}, where m is a odd number not ending with 5 and K is a natural number,

**Last two digits will always be (2×m +50)**.For all the remaining cases, the last two digits of N

^{40k+x},

**Last two digits will always be equal to the last 2 digits of N**^{x}

**Question 1**Find the last two digits of 12345

^{98745}.

05 | 00 |

25 | 50 |

**Question 2**Find the last two digits of 39

^{2}.

21 | 81 |

79 | 67 |

**Question 3**Find the last two digits of 22

^{482}.

84 | 48 |

92 | 64 |

**Question 4**Find the last two digits of 42

^{801}.

29 | 92 |

45 | 54 |

**Question 5**Find the last two digits of 39

^{900}.

01 | 81 |

27 | 34 |

**Question 6**Find the last two digits of 53

^{2}.

01 | 02 |

03 | 04 |

**Question 7**Find the last two digits of 81

^{2}.

21 | 61 |

27 | 67 |

**Question 8**Find the last two digits of 80

^{754}.

64 | 16 |

00 | 08 |