A group of digits, denoting a number is called a numeral.

E.g. 123 |
of 1 | of 2 | 3 |
---|---|---|---|

Face Value | 1 | 2 | 3 |

Place Value | 100 | 20 | 3 |

Natural | Counting numbers 1, 2, 3, 4, … |
---|---|

Whole | 0, 1, 2, 3, … [all counting numbers with zero] |

Integers | Positive: {1, 2, 3, 4, …}; Negative Integers: {-1, -2, -3, …}; Non-Positive & Non-Negative Integers: 0 |

Even | 2, 4, 6, 8, … [A number divisible by 2] |

Odd | 1, 3, 5, 7, … [A number not divisible by 2] |

Prime |
[>1 & has exactly two factors, namely 1 and the number itself]. Up to 100: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97} #25 prime numbers. Greater 100: 191 is not divisible by 2, 3, 5, 7, 11, 13 |

Composite | 4, 6, 8, 9, … [>1 & not prime] |

Co-prime | (2,3), (4,5), (7,9), (8,11), etc. [H.C.F is 1] |

By | Condition | Example |
---|---|---|

2 | Unit digit will be any of 0, 2, 4, 6 or 8. | 2402 |

3 | Sum of all digits divisible by 3. | 312. 3 + 1 + 2 = 6. |

4 | Last 2 digits divisible by 4. | 2316 |

5 | Unit digit is either 0 or 5. | 505 |

6 | Divisible by both 2 and 3. | 18 |

8 | Last 3 digits divisible by 8. | 1288 |

9 | Sum of all digits divisible by 9. | 504. 5 + 0 + 4 = 9. |

10 | Unit digit should be 0. | 5340 |

11 | Difference of sum of odd place digits & even place digits is either 0 or divisible by 11. | 6402. [(2 + 4) - (0 + 6)] = 0 |

1 | (1+2+3+...+n) = n(n+1)/2 |

2 | (1^{2}+2^{2}+3^{2}+...+n^{2}) = [n(n+1)(2n+1)]/6 |

3 | (1^{3}+2^{3}+3^{3}+...+n^{3}) = [n^{2}(n+1)^{2}]/4 |

Sat, 25 May

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