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# Number Theory - SHS

### Number Theory and Divisibility - SHS Freshmen Math Team

Question | Answer |
---|---|

Divisibility Rule: 2 | The last digit is even |

Divisibility Rule: 3 | The sum of the digits is divisible by three |

Divisibility Rule: 4 | The last two digits are divisble by 4 (#: abc, bc is divisible by 4) |

Divisibility Rule: 5 | The last digit is 5 or 0 |

Divisibility Rule: 6 | The number is divisible by both 2 and 3 |

Divisibility Rule: 7 | Double the last digit and subract from the rest of the number, if the result is divisible by7, then the number is divisble by 7 (#: abc, ab-2c is divisible by 7) |

Divisibility Rule: 8 | The number is divisible by both 2 and 4 |

Divisibility Rule: 9 | The sum of the digits is divisible by 3 |

Number Cycles: Powers of 2 | 4 cycles: 2,4,8,6 |

Number Cycles: Powers of 3 | 4 cycles: 3,9,7,1 |

Number Cycles: Powers of 4 | 2 cycles: 4,6 |

Number Cycles: Powers of 5 | Always ends in 5 |

Number Cycles: Powers of 6 | Always ends in 6 |

Number Cycles: Powers of 7 | 4 cycles: 7,9,3,1 |

Number Cycles: Powers of 8 | 4 cycles: 8,4,2,6 |

Number Cycles: Powers of 9 | 2 cycles: 9,1 |

Prime Number | A Number whose only factors are 1 and itself |

Composite Number | A Number who has more factor pairs than just 1 and itself |

Abundant Number | A Number whose value is less than the sum of its factors (excluding itself) |

LCM | Least Common Multiple, The lowest number that is divisible by both numbers in the given pair |

GCD | Greatest Common Divisor, the greatest number that both numbers in a given pair are divisible by |

Trailing Zeroes | Chains of zeroes that occupy the farthest right digits in a (Usually long) number |

The Number of Trailing Zeroes (x=#) | 10^x |

Prime Numbers Less Than 100 | 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,51,53,59,61,67,71,73,79,83,87,89,97 |

6 Factorial (Expanded Form) | 6*5*4*3*2*1 = 720 |

Created by:
Vingkan