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) |
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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 |
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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 |
56 |
60 |
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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) |
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Divisible by 6?
| Rule: If it is divisible by 2 and by 3 |
 |
| Number |
Divisible? |
Why? |
| 5,106 |
Yes |
The last digit is a 2 (it is a multiple of 2 ) and...
5 + 1 + 0 + 6 = 12 (12 is a multiple of 3) |
| 636 |
Yes |
The last digit is a 6 (it is a multiple of 2 ) and...
6 + 3 + 6 = 15 (15 is a multiple of 3) |
| 5,912 |
No |
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) |
| 508 |
No |
The last digit is a 8 (it is a multiple of 2 ) but...
5 + 0 + 8 = 13 (13 is not a multiple of 3) |
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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 |
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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) |
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