This page is the result of my work to find out as many divisibility tricks as possible. I worked for days to come up with most of these, however I adopted just a few of them.

Throughout the table, a few different procedures will be used. They are listed below:

Procedure 1- Divide digits of the number into groups of `a`. Add all the groups together. If the sum is divisible by `n`, then the number is divisible by `n`.

Procedure 2- Divide digits of the number into groups of `a`. Add every other group together, then add the remaining groups together. Find the difference of the two sums and if that is divisible by `n`, then the number is divisible by `n`.

Examples of each appears below the table.

If the number "Method" then number is divisible by n. | |
---|---|

n | Method |

2 | last digit is even |

3 | Procedure 1: a=1 |

4 | has its last 2 digits divisible by 4 |

5 | ends in 0 or 5 |

6 | is divisible by 2 and 3 |

7 | Procedure 2. a=3 |

8 | has its last 3 digits divisible by 8 |

9 | Procedure 1. a=1 |

10 | ends in 0 |

11 | Procedure 1. a=2 |

12 | is divisible by 3 and 4 |

13 | Procedure 2. a=3 |

14 | is divisible by 2 and 7 |

15 | is divisible by 3 and 5 |

16 | has its last 4 digits divisible by 16 |

17 | Procedure 2: a=8 |

18 | is divisible by 2 and 9 |

19 | Procedure 2: a=9 |

20 | last digit is zero and tens digit is even |

21 | is divisible by 3 and 7 |

22 | is divisible by 2 and 11 |

23 | Procedure 2: a=11 |

24 | is divisible by 3 and 8 |

25 | ends in 00, 25, 50, or 75 |

26 | is divisible by 2 and 13 |

27 | Procedure 1: a=3 |

28 | is divisible by 4 and 7 |

29 | Procedure 2: a=14 |

30 | is divisible by 3 and 10 |

31 | Procedure 1: a=15 |

32 | has its last 5 digits divisible by 32 |

33 | is divisible by 3 and 11 |

34 | is divisible by 2 and 17 |

35 | is divisible by 5 and 7 |

36 | is divisible by 4 and 9 |

37 | Procedure 1: a=3 |

38 | is divisible by 2 and 19 |

39 | is divisible by 3 and 13 |

40 | ends in zero, two digits to left of zero are divisible by 4 |

41 | Procedure 1: a=5 |

42 | is divisible by 2, 3, and 7 |

43 | Procedure 1: a=21 |

44 | is divisible by 4 and 11 |

45 | is divisible by 5 and 9 |

46 | is divisible by 2 and 23 |

47 | Procedure 2: a=23 |

48 | is divisible by 3 and 16 |

49 | Procedure 2: a=21 |

50 | ends in 00 or 50 |

51 | is divisible by 3 and 17 |

52 | is divisible by 4 and 13 |

53 | Procedure 1: a=13 |

54 | is divisible by 2 and 27 |

55 | is divisible by 5 and 11 |

56 | is divisible by 7 and 8 |

57 | is divisible by 3 and 19 |

58 | is divisible by 2 and 29 |

59 | Procedure 2: a=29 |

60 | is divisible by 3 and 20 |

61 | Procedure 2: a=30 |

62 | is divisible by 2 and 31 |

63 | is divisible by 7 and 9 |

64 | has its last 6 digits divisible by 64 |

65 | is divisible 5 and 13 |

66 | is divisible by 2, 3, and 11 |

67 | Procedure 1: a=33 |

68 | is divisible by 4 and 17 |

69 | is divisible by 3 and 23 |

70 | is divisible by 7 and 10 |

71 | Procedure 1: a=35 |

72 | is divisible by 8 and 9 |

73 | Procedure 1: a=4 |

74 | is divisible by 2 and 37 |

75 | is divisible by 3 and 25 |

76 | is divisible by 4 and 19 |

77 | is divisible by 7 and 11 |

78 | is divisible by 2, 3, and 13 |

79 | Procedure 1: a=13 |

80 | ends in zero, three digits to left of zero are divisible by 8 |

81 | Procedure 1: a=9 |

82 | is divisible by 2 and 41 |

83 | Procedure 1: a=41 |

84 | is divisible by 3, 4, and 7 |

85 | is divisible by 5 and 17 |

86 | is divisible by 2 and 43 |

87 | is divisible by 3 and 29 |

88 | is divisible by 8 and 11 |

89 | Procedure 1: a=44 |

90 | is divisible by 9 and 10 |

91 | is divisible by 7 and 13 |

92 | is divisible by 4 and 23 |

93 | is divisible by 3 and 31 |

94 | is divisible by 2 and 47 |

95 | is divisible by 5 and 19 |

96 | is divisible by 3 and 32 |

97 | Procedure 2: a=48 |

98 | is divisible by 2 and 49 |

99 | Procedure 1: a=2 |

100 | ends in 00 |

101 | Procedure 2: a=2 |

102 | is divisible by 2, 3 and 17 |

Examples of procedures 1 and 2:

One would use procedure 1 if he wanted to check for divisibility by 11. Say the number 257 513 575. First divide it into groups of 2 (since `a`=2) like this: 02, 57, 51, 35, 75. Then add them all up like this: 02 + 57 + 51 + 35 + 75 = 220. Since 220 is divisible by 11, 257 513 575 must be divisible by 11.

One would use procedure 2 if he wanted to check for divisibility by 7. Say the number 9 876 543 210. First divide it into groups of 3 (since `a`=3) like this: 009, 876, 543, 210. Find the sums of everyother group like this: 009 + 543 = 552 & 876 + 210 = 1086. Now find the difference id est: 1086 - 552 = 534. Since 534 is not divisible by 7, 9 876 543 210 is not divisible by 7.

Last Updated: 2009-05-02

The author, Marq Thompson, wished the content of this website to be uncopyrighted after his death.