Tool to list multiples of a number. A multiple of a number is another number calculated with the product of this number by an integer.

Multiples of a Number - dCode

Tag(s) : Arithmetics, Series

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Tool to list multiples of a number. A multiple of a number is another number calculated with the product of this number by an integer.

Take a number and multiply it by a quantity/factor/coefficient (2, 3, 4 etc.) to get a multiple.

It exists **an infinite number of multiples**, so it is impossible to **list all multiples** of a given number, dCode suggest to fix an upper and lower bound (all multiples between A and B).

__Example:__ $ N = 3 $, so $ N \times 2 = 6 $, $ 6 $ is a multiple of $ 3 $,

$ N \times 3 = 9 $, $ 9 $ is a multiple of $ 3 $, etc.

Multiples of 1 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... |

Multiples of 2 | 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ... |

Multiples of 3 | 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ... |

Multiples of 4 | 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ... |

Multiples of 5 | 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ... |

Multiples of 6 | 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ... |

Multiples of 7 | 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, ... |

Multiples of 8 | 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ... |

Multiples of 9 | 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ... |

Multiples of 10 | 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ... |

Multiples of 11 | 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, ... |

Multiples of 12 | 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ... |

Multiples of 13 | 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, ... |

Multiples of 14 | 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ... |

Multiples of 15 | 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ... |

For school multiplications, use a calculator here (link)

Divide A by B, if the rest of the Euclidean division is 0, then A is a multiple of B, and B is a divisor of A.

__Example:__ Is 60 a **multiple of 4**? Divide 60 by 4, 60/4 = 15 (integer without decimals after the decimal point), remain 0, so 60 is a **multiple of 4** and 4 is a divisor of 60.

__Example:__ Is 22 a **multiple of 4**? Divide 22 by 4, 22/4 = 5.5 (non-integer number, with decimals after decimal point) ie 22/4 = 5 + remainder 2, so 22 is not a **multiple of 4** and 4 is not a divisor of 22.

Yes, in theory, 0 is multiple of all numbers because whatever $ n $, $ 0 / n = 0 $. In practice, it is often omitted from the **list of multiples**.

Zero is a multiple of every integer (except itself)

Yes, all numbers are **multiples of 1**, but it is wrong to say that 1 is a multiple of all numbers, but it is true to say that 1 is a divisor of all numbers.

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