# What number is divisible by 871?

## Meinstein

The **Divisibility rules** for natural numbers show quickly whether and how a natural number can be divided.

### regulate

The number is ...

divisible by | Divisibility rule |

2 | if its last digit is a 0 or an even number. |

3 | if the checksum is divisible by 3, |

4 | if its last two digits result in a number that is divisible by 4. |

5 | if its last digit is a 0 or 5, |

6 | if the number is divisible by 2 and by 3 |

7 | see below. |

8 | if the number formed from the last three digits is divisible by 8. |

9 | if your checksum is divisible by 9 |

10, 100, 1000… | if your last digit is 0, 00, 000…. |

11 | see below |

12 | if the number is divisible by 3 and by 4. |

15 | if the number is divisible by 3 and by 5. |

25 | if the number from the last two digits is divisible by 25. |

30 | if the last digit is a zero and is divisible by 3 without this last digit. |

40 | if the last digit is a zero and is divisible by 4 without this last digit. |

50 | if the last digit is a zero and without this is divisible by 5. |

125 | if the number from the last three digits is divisible by 125. |

### Divisible by 7

We divide the number into two parts: b is the last digit, a are the digits in front of it.

8715 → 871 (a) and 5 (b)

We subtract b from a two times:

871 – 10 = 861

We repeat this process until we get a number that we can figure out in our head whether it is divisible by 7.

86 – 2 = 84

Since 84 is divisible by 7, it's 8715 too.

### Divisible by 11

A number is divisible by 11 if the alternating checksum is divisible by 11.

### Exercises

45 | The 5 indicates that the number is divisible by 5. Since the checksum is 9, 3 is also a factor. So 45 is also divisible by 15. |

115 | The number is divisible by 5 but not by 15. |

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