Hi Ho!(adsbygoogle = window.adsbygoogle || []).push({});

It is easy to observe that to get all factors of an integern, one does not need to try whetheradividesnfor 1 <a<n.

But, rather using the following observation:

Supposenis 24, then

24 / 1 = 24

24 / 2 = 12

24 / 3 = 8

24 / 4 = 6

-------------(!)

24 / 6 = 4

24 / 8 = 3

24 / 12 = 2

24 / 24 = 1

Notice that after (!), the divisor and the result of each probing step are just the swap of the divisor and the result of each probing step before (!). With other words, (!) acts as a mirror. Therefore, to find all factors of an integern, one only needs to record both the divisor and the result of each probing step until the first swap happens, or until the values of the divisor and the result are the same such as whenn= 49.

We know that, to test whether an integer numbernis prime or not, one only needs to try to dividenby an integer from 2 until square root ofn. Is it possible to predict before hand at what n-th factor the mirroring will occur?

Thanks.

Regards,

Eus

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The limit of a factoring algorithm

Loading...

Similar Threads - limit factoring algorithm | Date |
---|---|

I Factorization of a matrix equation | Oct 20, 2016 |

Limit of two matrices each to the kth power and multiplied | Jul 4, 2013 |

Indeterminate limit of the form 1/0 | May 26, 2013 |

Understanding Direct and Inverse Limits | Nov 5, 2012 |

Is Physical Symmetry Limited Due To The Classification Theorem? | Apr 4, 2012 |

**Physics Forums - The Fusion of Science and Community**