D iv is ib il it y R u l e s
Divisible by 2?
Rule: If it ends with a 0, 2, 4, 6, or 8
Number
Divisible?
Why?
456
Yes
The last digit is 6
68
Yes
The last digit is 8
25
No
The last digit is 5 (not a 2,4,6,or 8)
207
No
The last digit is 7 (not a 2,4,6,or 8)
Divisible by 3?
Rule: If the sum of the digits is a multiple of 3
Number
Divisible?
Why?
405
Yes
4 + 0 + 5 = 9 (9 is a multiple of 3)
381
Yes
3 + 8 + 1 = 12 (12 is a multiple of 3)
928
No
9 + 2 + 8 = 19 (19 is not a multiple of 3)
4,616
No
4 + 6 + 1 + 6 = 17 (17 is not a multiple of 3)
Helper: The multiples of 3 include...
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
Divisible by 4?
Rule: If the last two digits are a multiple of 4
Number
Divisible?
Why?
348
Yes
48 is a multiple of 4
27,616
Yes
16 is a multiple of 4
8,514
No
14 is not a multiple of 4
722
No
22 is not a multiple of 4
Helper: The multiples of 4 include...
4
8
12
16
20
24
28
32
36
40
44
48
52
Divisible by 5?
Rule: If it ends with a 5 or a 0
Number
Divisible?
Why?
3,425
Yes
The last digit is 5
750
Yes
The last digit is 0
8,551
No
The last digit is 1 (not a 0 or a 5)
394
No
The last digit is 4 (not a 0 or a 5)
56
60
Divisible by 6?
Rule: If it is divisible by 2 and by 3
Number
Divisible?
5,106
Yes
5,912
No
Why?
The last digit is a 2 (it is a multiple of 2 ) and...
5 + 1 + 0 + 6 = 12 (12 is a multiple of 3)
The last digit is a 2 (it is a multiple of 2 ) but...
5 + 9 + 1 + 2 = 17 (17 is not a multiple of 3)
Divisible by 9?
Rule: If the sum of the digits are a multiple of 9
Number
Divisible?
Why?
7,686
Yes
7 + 6 + 8 + 6 = 27 (27 is a multiple of 9)
252
Yes
2 + 5 + 2 = 9 (9 is a multiple of 9)
883
No
8 + 8 + 3 = 19 (19 is not a multiple of 9)
5,105
No
5 + 1 + 0 + 5 = 11 (11 is not a multiple of 9)
Helper: The multiples of 9 include...
9
18
27
36
45
54
63
72
81
90
99
108
117
126
135
Divisible by 10?
Rule: If the last digit is 0
Number
Divisible?
Why?
880
Yes
The last digit is 0
9,560
Yes
The last digit is 0
312
No
The last digit is 2 (not a 0)
7,897
No
The last digit is 7 (not a 0)