The document outlines rules for determining if a number is divisible by 1-10. The rules are: 1) All numbers are divisible by 1 2) The last digit must be even or 0 3) The sum of the digits must be divisible by the number 4) The last two digits must form a number divisible by the number 5) The last digit must be a 5 or 0 6) The number must be divisible by both 2 and 3 7) The last three digits must form a number divisible by the number 8) The sum of the digits must be divisible by the number 9) The number must end in 0

1. 7-1 Rules of Divisibility
Math Notes
Number Sense 4.1

2. Divisible by: Rule
1 All numbers are divisible by 1

3. Divisible by: Rule
1 All numbers are divisible by 1
2 The last digit of the number is even or 0

5. 54 8
90

6. 54 8
90
All even numbers.

7. 27 4
2 54 28
45
2 90
All even numbers.

8. 27 4
2 54 28
45
2 90
54, 90, 8 are
All even numbers.
divisible by 2.

9. Divisible by: Rule
1 All numbers are divisible by 1
2 The last digit of the number is even or 0
3 The sum of the digits is divisible by 3

10. 37

11. 3+7

12. 3 + 7 = 10

13. 3 +7= 10

14. 3 r1
3 +7= 3 10
9
1

15. 3 r1
3 +7= 3 10
9
37 is NOT 1
divisible by 3

16. 69

17. 6+9

18. 6 + 9 = 15

19. 6 +9= 15

20. 5
6 +9= 3 15
15
0

21. 5
6 +9= 3 15
15
69 is 0
divisible by 3

22. Divisible by: Rule
1 All numbers are divisible by 1
2 The last digit of the number is even or 0
3 The sum of the digits is divisible by 3
4 The last two digits form a number divisible by 4

23. 4 29324

24. 7331
4 29324
28
13
12
12
12
04
4

25. 7331
4 29324
OR
28
13
12
12
12
04
4

26. 4 29324

27. 4 29324

28. 4 24

29. 6
4 24
24
0

30. Divisible by: Rule
1 All numbers are divisible by 1
2 The last digit of the number is even or 0
3 The sum of the digits is divisible by 3
4 The last two digits form a number divisible by 4
5 The last digit is a 5 or 0

32. 45 25
70

33. 45 25
70
All numbers ending
in 5 or 0.

34. 9 5
5 45 5 25
14
5 70
All numbers ending
in 5 or 0.

35. 9 5
5 45 5 25
14
5 70
All numbers ending 45, 70, 25 are
in 5 or 0. divisible by 5.

36. Divisible by: Rule
1 All numbers are divisible by 1
2 The last digit of the number is even or 0
3 The sum of the digits is divisible by 3
4 The last two digits form a number divisible by 4
5 The last digit is a 5 or 0
6 The number is divisible by both 3 AND 2

37. If divisible by 2 AND 3,
18 is divisible by 6.

38. 18
If divisible by 2 AND 3,
18 is divisible by 6.

39. 9
2 18
If divisible by 2 AND 3,
18 is divisible by 6.

40. 9
2 18
18
If divisible by 2 AND 3,
18 is divisible by 6.

41. 9
2 18
1+8
If divisible by 2 AND 3,
18 is divisible by 6.

42. 9
2 18
1+8 = 9
If divisible by 2 AND 3,
18 is divisible by 6.

43. 9
2 18
1+8 = 9
If divisible by 2 AND 3,
18 is divisible by 6.

44. 9
2 18 3
1+8 = 3 9
9
If divisible by 2 AND 3,
18 is divisible by 6. 0

45. Divisible by: Rule
1 All numbers are divisible by 1
2 The last digit of the number is even or 0
3 The sum of the digits is divisible by 3
4 The last two digits form a number divisible by 4
5 The last digit is a 5 or 0
6 The number is divisible by both 3 AND 2
8 The last three digits form a number divisible by 8

46. 8 25272

47. 3 1 59
8 25272
24
12
8
47
40
72
72

48. 3 1 59
8 25272
OR
24
12
8
47
40
72
72

49. 8 25272

50. 8 25272

51. 8 272

52. 34
8 272
24
32
32

53. Divisible by: Rule
1 All numbers are divisible by 1
2 The last digit of the number is even or 0
3 The sum of the digits is divisible by 3
4 The last two digits form a number divisible by 4
5 The last digit is a 5 or 0
6 The number is divisible by both 3 AND 2
8 The last three digits form a number divisible by 8
9 The sum of the digits is divisible by 9

54. 56

55. 5+6

56. 5 + 6 = 11

57. 5 +6= 11

58. 1 r2
5 +6= 9 11
9
2

59. 1 r2
5 +6= 9 11
9
56 is NOT 2
divisible by 9

60. 99

61. 9+9

62. 9 + 9 = 18

63. 9 +9= 18

64. 2
9 +9= 9 18
18
0

65. 2
9 + 9 = 9 18
18
99 is divisible 0
by 9

66. Divisible by: Rule
1 All numbers are divisible by 1
2 The last digit of the number is even or 0
3 The sum of the digits is divisible by 3
4 The last two digits form a number divisible by 4
5 The last digit is a 5 or 0
6 The number is divisible by both 3 AND 2
8 The last three digits form a number divisible by 8
9 The sum of the digits is divisible by 9
10 The number ends in 0

68. 70 20
90

69. 70 20
90
All even numbers.

70. 27 4
2 70 2 20
45
2 90
All even numbers.

71. 27 4
2 70 2 20
45
2 90
54, 90, 8 are
All even numbers.
divisible by 2.