Test for divisibility by 2 |
The last digit should be divisible by 2. |
Examples: 24,42,88,566 |

Test for divisibility by 3 |
The sum of digits should be divisible by 3. |
Let us take 15. Sum=1+5=6. 6 is divisible by 3. Hence 15 is divisible by 3. Assume a 5 digit number.. Let us take 23453. Sum=2+3+4+5+3=17. Since 17 is not divisible by 3. Hence 23453 is not divisible by 3. |

Test for divisibility by 4 |
The number formed with its last 2 digits should be divisible by 4. |
Let us take 456544. In this number last two digits i.e. 44 is divisible by 4. Hence the number 45644 is divisible by 4. |

Test for divisibility by 5 |
The last number should be divisible by 5 i.e. It should either be 0 or 5. |
Let us take 459990. Since the number ends with 0, it is divisible by 5. |

Test for divisibility by 6 |
It should be divisible by both 2 and 3. |
Let us take 144 which is both divisible by 2 & 3. Hence it is divisible by 6 also. |

Test for divisibility by 7 |
Subtract two times the unit digit from the remaining number. If it is 0 or divisible by 7, then the number is also divisible by 7. |
Let us take : 2793 Unit digit=3.Hence, 3*2= 6 Subtracting 279-6= 273 now unit digit=3.Hence, 3*2=6.Subtracting, 27-6= 21 which is divisible by 7 so 2793 is also divisible by 7. |

Test for divisibility by 8 |
The number formed by its last 3 digits should be divisible by 8. |
Let us take 678396. Check for the last three digits i.e 396 which is divisible by 8. Hence, 678396 is divisible by 8. |

Test for divisibility by 9 |
The sum of the digits should be divisible by 9. |
Let us take 345654. Sum=3+4+5+6+5+4=27 Since 27 is divisible by 9. Hence, 345654 is divisible by 9. |

Test for divisibility by 10 |
The last digit should be 0. |
80,100010,8090,8900,980980 |

Test for divisibility by 11 |
Subtract the unit digit from the remaining number. |
Let us take 132. The unit digit is 2.Subtract 2 from 13 i.e. the remaining number we get 11 which is divisible by 11. Hence 132 is divisible by11. |

Test for divisibility by 13 |
Add four times the unit digit to the remaining number. |
Let us take 117. Four times the unit digit =4*7 which is 28 Adding, 11+28=39. Since 39 is divisible by 13. Hence,117 is divisible by 13. |

Test for divisibility by 17 |
Subtract five times the unit digit from the remaining number. |
Let us take 187. Five times the unit digit=5*7 which is 35. Subtracting, 35-18=17(since 35 is greater then 17). Hence 187 is divisible by 17. |

Test for divisibility by 19 |
Add two times the unit digit to the remaining number. |
Let us take 399. Two times the unit digit =9*2 which gives 18. Adding 39+18=57, which is divisible by 399. Hence 399 is divisible by 19. |

Test for divisibility by 23 |
Add seven times the unit digit to the remaining number. |
Let us take 207. Seven times unit digit =7*7 which gives 49 Adding 20+49=69 which is divisible by 23.Hence, 207 is divisible by 23. |