Divisible by

If

Example

2 
The last digit is even (0,2,4,6,8)

112 (Last digit is 2, which is even)  Yes
113 (Last digit is 3, which is not even)  No 
4 
The last two digit is divisible by 4

112 (Last 2 digit is 12, which is divisible by 4)  Yes
113 (Last 2 digit is 13, which is not divisible by 4)  No 
8 
The last three digit is divisible by 8

5816 (Last 3 digit is 816, which is divisible by 8)  Yes
5817 (Last 3 digit is 817, which is not divisible by 8)  No 



3 
The sum of the digits is divisible by 3

396 (3+9+6 = 18, which is divisible by 3)  Yes
397 (3+9+7 = 19, which is not divisible by 3)  No 
9 
The sum of the digits is divisible by 9

396 (3+9+6 = 18, which is divisible by 9)  Yes
397 (3+9+7 = 19, which is not divisible by 9)  No 



5 
The last digit is 0 or 5

105 (Last digit is 5)  Yes
106 (Last digit is 6)  No 
10 
The number ends in 0

150 (Last digit is 0)  Yes
151 (Last digit is 1)  No 



11 (method1) 
(sum of all odd place digit)  (sum of all even place digit) is 0 or divisible by
11. 
2563 [(2+6)  (5+3) = 0, which is 0]  Yes
7392 [(7+9)  (3+2) = 11, which is divisible by 11]  Yes
7393 [(7+9)  (3+3) = 10, which is not divisible by 11]  No 
11 (method2) 
Subtract the last digit from the rest of the number.
If the answer is divisible by 11, then original number is also visible by 11.
(Apply this rule to the answer again if necessary)

Check 2563 is divisible by 11 or not
2563 ⇒ 256  3 = 253
253 ⇒ 25  3 = 22
Here 22 is divisible by 11
So 2563 is divisible by 11
Check 7393 is divisible by 11 or not
7393 ⇒ 739  3 = 736
736 ⇒ 73  6 = 67
Here 67 is not divisible by 11
So 7393 is not divisible by 11




7 
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then original number is also visible by 7.
(Apply this rule to the answer again if necessary) 
Check 9464 is divisible by 7 or not
9464 ⇒ 946  4 × 2 = 946  8 = 938
938 ⇒ 93  8 × 2 = 93  16 = 77
Here 77 is divisible by 7
So 9464 is divisible by 7

13 
4 times the last digit and add it to the rest of the number.
If the answer is divisible by 13, then original number is also visible by 13.
(Apply this rule to the answer again if necessary).

Check 13273 is divisible by 13 or not
13273 ⇒ 1327 + 3 × 4 = 1327 + 12 = 1339
1339 ⇒ 133 + 9 × 4 = 133 + 36 = 169
169 ⇒ 16 + 9 × 4 = 16 + 36 = 52
Here 52 is divisible by 13
So 13273 is divisible by 13

17 
5 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 17, then original number is also visible by 17.
(Apply this rule to the answer again if necessary).

Check 17544 is divisible by 17 or not
17544 ⇒ 1754  4 × 5 = 1754  20 = 1734
1734 ⇒ 173  4 × 5 = 173  20 = 153
153 ⇒ 15  3 × 5 = 15  15 = 0
Here 0 is divisible by 17
So 17544 is divisible by 17

19 
2 times the last digit and add it to the rest of the number.
If the answer is divisible by 19, then original number is also visible by 19.
(Apply this rule to the answer again if necessary).

Check 19456 is divisible by 19 or not
19456 ⇒ 1945 + 6 × 2 = 1945 + 12 = 1957
1957 ⇒ 195 + 7 × 2 = 195 + 14 = 209
209 ⇒ 20 + 9 × 2 = 20 + 18 = 38
Here 38 is divisible by 19
So 19456 is divisible by 19

23 
7 times the last digit and add it to the rest of the number.
If the answer is divisible by 23, then original number is also visible by 23.
(Apply this rule to the answer again if necessary).

Check 29946 is divisible by 23 or not
29946 ⇒ 2994 + 6 × 7 = 2994 + 42 = 3036
3036 ⇒ 303 + 6 × 7 = 303 + 42 = 345
345 ⇒ 34 + 5 × 7 = 34 + 35 = 69
Here 69 is divisible by 23
So 29946 is divisible by 23

29 
3 times the last digit and add it to the rest of the number.
If the answer is divisible by 29, then original number is also visible by 29.
(Apply this rule to the answer again if necessary).

Check 37758 is divisible by 29 or not
37758 ⇒ 3775 + 8 × 3 = 3775 + 24 = 3799
3799 ⇒ 379 + 9 × 3 = 379 + 27 = 406
406 ⇒ 40 + 6 × 3 = 40 + 18 = 58
Here 58 is divisible by 29
So 37758 is divisible by 29




31 
3 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 31, then original number is also visible by 31.
(Apply this rule to the answer again if necessary).


37 
11 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 37, then original number is also visible by 37.
(Apply this rule to the answer again if necessary).


41 
4 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 41, then original number is also visible by 41.
(Apply this rule to the answer again if necessary).


43 
13 times the last digit and add it to the rest of the number. If the answer is divisible
by 43, then original number is also visible by 43.
(Apply this rule to the answer again if necessary).




