# Applying Negative Remainders ## 9 thoughts on “Applying Negative Remainders”

1. nikunjbehani007 |

This negative remainder concept really saves a lot of time !

2. sanchi |

find the remainder when 24^60 + 60^24 /84?

3. catcracker |

Sanchi, rather than solving I will give you a hint. Take 12 common in numerator and denominator so you are left with (2 * 24^59 + 5 * 60^23) / 7. This should be easy to solve – find the answer and multiply by 12.

regards
J

• AA |

Answer should be 24, right?

24^60 = 12^60 * 2^60 div by 12*7 => 12 * Rem (2^60/7) => rem = 12*1 = 12

60^ 24 = 12^60 * 5^60 div by 12*7 => 12* Rem (5^60/7) => rem = 12* (-1)^20 = 12

Hence, (12+12) div by 84 gives the total remainder => Remainder = 24

• catcracker |

Not quite, you’ve made a slight error!
You wrote:
24^60 = 12^60 * 2^60 div by 12*7 => 12 * Rem (2^60/7) => rem = 12*1 = 12
But actually
24^60 = 12^60 * 2^60 div by 12*7 => 12 * Rem [(12^59 * 2^60)/7] => rem = 12*3 = 36
Similarly the other also will give 36 and hence the overall remainder will turn out to be 72.

regards
J

• kronos |

Is the answer 1?

4. gaurav raj |

is the answer for Sanchi’s question 72?

5. Rohan |

How can to identify when to apply the “Applying Negative Remainders”. Say for example 23456^34567 divided by 13.

• catcracker |

So if you are dividing by 13, just start the normal procedure and keep going till you reach either 1 or 2. If you reach one, your job is done, if you reach 12, treat it as -1 and continue (otherwise you would have to go twice as far to reach 1). Deal on a case-by-case basis!

regards
J