In this article we will learn some new and easy tricks to divide large numbers by prime numbers using concept of seed numbers. We had earlier written an article on the prime number divisibility rules using some rules, to check this article please refer to this links

http://readin.net/prime-number-divisibility-rules/

Prime Number: The prime numbers are the numbers that have only 2 factors; 1 and number itself. Apart from 2 all the prime numbers are odd numbers

Seed Number: Every prime number (apart from 2) has 2 seed number, the trick to find out the seed number is as follows:

- Find out the multiples of the prime number ending in 1 and 9 for eg. 7 x 3 = 21 and 7 x 7 = 49.
- Now write numbers in the factors of 10 with + or – for eg. 21 = 2 x10 + 1 & 49 = 5 x 10 – 1
- so the seed numbers of 7 are 2 and 5
**IMP NOTE : The seed number received from + 1 are always negative and seed number received from – 1 are always taken as positive .**So in the above example the seed number are -2 and 5

How to use this concept:

Lets check if 10754 is divisible by 19.

- The seed no. of 19 are -17 & 2, you can use any seed no. the result will be same
- Multiple unit digit by a seed no. ( 2 x 4) and add to rest of the number 1075 so we have 8 + 1075 = 1083
- To get smaller number we can repeat this step 3 x 2 + 108= 6 +108 = 114 and we know 19 x 6 = 114

### Seed numbers of common Prime numbers

Prime Number | Multiples ending in 1 | Multiples ending in 9 | Seed Number |
---|---|---|---|

3 | 21 = 2 × 10 + 1 | 9 = 1 × 10 – 1 | – 2, 1 |

7 | 21 = 2 × 10 + 1 | 49 = 5 × 10 – 1 | – 2, 5 |

13 | 91 = 9 × 10 + 1 | 39 = 4 × 10 – 1 | – 9, 4 |

17 | 51 = 5 × 10 + 1 | 119 = 12 × 10 – 1 | – 5, 12 |

19 | 171 = 17 × 10 + 1 | 19 = 2 × 10 – 1 | – 17, 2 |

23 | 161 = 16 x 10 + 1 | 69 = 7 x 10 – 1 | -16, 7 |

29 | 261 = 26 x 10 + 1 | 29 = 3 x 10 – 1 | -26, 3 |

31 | 31 = 3 x 10 + 1 | 279 = 28 x 10 – 1 | -3, 28 |

37 | 111 = 11 x 10 + 1 | 259 = 26 x 10 – 1 | -11, 26 |

41 | 41 = 4 x 10 + 1 | 369 = 37 x 10 -1 | -4, 37 |

The seed numbers of the some key prime numbers are provided here

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