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Home > Pre-Algebra calculators > Divisibility rule example
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  1. Formula
  2. Divisibility rule of 2 example
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2. Divisibility rule of 2 example
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1. Formula


These rules let you test if one number is divisible by another, without having to do too much calculation!
Number Divisible by Rule Example
ABCDEF 2 If 'F' is even 112 (Last digit is 2, which is even)
ABCDEF 3 If 'A+B+C+D+E+F' is divisible by 3 396 (3+9+6 = 18, which is divisible by 3)
ABCDEF 4 If 'EF' is divisible by 4 112 (Last 2 digit is 12, which is divisible by 4)
ABCDEF 5 If 'F' is 0 or 5 105 (Last digit is 5)
ABCDEF 6 If 'ABCDEF' is divisible by 2 and 3
ABCDEF 7 If 'ABCDE - 2×F' is divisible 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
ABCDEF 8 If 'DEF' is divisible by 8 5816 (Last 3 digit is 816, which is divisible by 8)
ABCDEF 9 If 'A+B+C+D+E+F' is divisible by 9 396 (3+9+6 = 18, which is divisible by 9)
ABCDEF 10 If 'F' is 0 150 (Last digit is 0)
ABCDEF 11
(method-1)		 (Sum of digits in odd positions) - (Sum of digits in even positions) is 0 or divisible by 11. 2563 = [(5+3) - (2+6) = 0, which is 0]
7392 = [(3+2) - (7+9) = -11, which is divisible by 11]
ABCDEF 11
(method-2)		 If 'ABCDE - F' is divisible 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
ABCDEF 12 If 'ABCDEF' is divisible by 3 and 4
ABCDEF 13 If 'ABCDE + 4×F' is divisible 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
ABCDEF 14 If 'ABCDEF' is divisible by 2 and 7
ABCDEF 15 If 'ABCDEF' is divisible by 3 and 5
ABCDEF 16 If 'CDEF' is divisible by 16 10256 (Last 4 digit is 0256, which is divisible by 16) - Yes
10255 (Last 4 digit is 0255, which is not divisible by 16) - No
ABCDEF 17 If 'ABCDE - 5×F' is divisible 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
ABCDEF 18 If 'ABCDEF' is divisible by 2 and 9
ABCDEF 19 If 'ABCDE + 2×F' is divisible 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
ABCDEF 20 If 'ABCDEF' is divisible by 4 and 5
ABCDEF 21 If 'ABCDEF' is divisible by 3 and 7
ABCDEF 22 If 'ABCDEF' is divisible by 2 and 11
ABCDEF 23 If 'ABCDE + 7×F' is divisible 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
ABCDEF 24 If 'ABCDEF' is divisible by 3 and 8
ABCDEF 25 If 'EF' is divisible by 25
ABCDEF 26 If 'ABCDEF' is divisible by 2 and 13
ABCDEF 27 If 'ABCDE - 8×F' is divisible by 27
(Apply this rule to the answer again if necessary).
ABCDEF 28 If 'ABCDEF' is divisible by 4 and 7
ABCDEF 29 If 'ABCDE + 3×F' is divisible 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
ABCDEF 30 If 'ABCDEF' is divisible by 2,3 and 5
ABCDEF 31 If 'ABCDE - 3×F' is divisible by 31
(Apply this rule to the answer again if necessary). 		Check 2263 is divisible by 31 or not
`2263=>226 - 3 xx 3 = 226 -9 = 217`
`217=>21 - 7 xx 3 = 21 -21 = 0`
Here 0 is divisible by 31.
So 2263 is divisible by 31.
ABCDEF 32 If 'BCDEF' is divisible by 32
ABCDEF 33 If 'ABCDEF' is divisible by 3 and 11
ABCDEF 34 If 'ABCDEF' is divisible by 2 and 17
ABCDEF 35 If 'ABCDEF' is divisible by 5 and 7
ABCDEF 36 If 'ABCDEF' is divisible by 4 and 9
ABCDEF 37 If 'ABCDE - 11×F' is divisible by 37
(Apply this rule to the answer again if necessary). 		Check 2701 is divisible by 37 or not
`2701=>270 - 1 xx 11 = 270 -11 = 259`
`259=>25 - 9 xx 11 = 25 -99 = -74`
Here -74 is divisible by 37.

So 2701 is divisible by 37.
ABCDEF 38 If 'ABCDEF' is divisible by 2 and 19
ABCDEF 39 If 'ABCDEF' is divisible by 3 and 13
ABCDEF 39 If 'ABCDE + 4×F' is divisible by 39
(Apply this rule to the answer again if necessary). 		Check 5226 is divisible by 39 or not
`522color{red}{6}=>522 + color{red}{6} xx 4 = 522 +24 = 546`
`54color{red}{6}=>54 + color{red}{6} xx 4 = 54 +24 = 78`
Here 78 is divisible by 39.
`:.` 5226 is divisible by 39.
ABCDEF 40 If 'ABCDEF' is divisible by 5 and 8
ABCDEF 41 If 'ABCDE - 4×F' is divisible by 41
(Apply this rule to the answer again if necessary). 		Check 2993 is divisible by 41 or not
`2993=>299 - 3 xx 4 = 299 -12 = 287`
`287=>28 - 7 xx 4 = 28 -28 = 0`
Here 0 is divisible by 41.

So 2993 is divisible by 41.
ABCDEF 42 If 'ABCDEF' is divisible by 2, 3 and 7
ABCDEF 43 If 'ABCDE + 13×F' is divisible by 43
(Apply this rule to the answer again if necessary). 		Check 3139 is divisible by 43 or not
`3139=>313 + 9 xx 13 = 313 +117 = 430`
`430=>43 + 0 xx 13 = 43 = 43`
Here 43 is divisible by 43.
So 3139 is divisible by 43.
ABCDEF 44 If 'ABCDEF' is divisible by 4 and 11
ABCDEF 45 If 'ABCDEF' is divisible by 5 and 9
ABCDEF 46 If 'ABCDEF' is divisible by 2 and 23



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