(1) 0 1 features:
1 is any integer divisor, i.e., for any integer a, total 1 | A
0 is any non-zero integer multiple of, a ≠ 0, a is an integer, A | 0 .
(2) If the last bit is an integer of 0,2,4,6 or 8, this number is divisible by 2.
(3) If an integer number of divisible by 3 and is an integer that is divisible by 3.
(4) If the end of a two-digit integer divisible by four, the number is divisible by 4.
(5) If the last bit is 0 or an integer of 5, then this number can be divisible by 5.
(6) If an integer divisible by 2 and 3, then the number can be divisible by 6.
(7) If a digit integer truncated, and then from the remaining numbers, subtracting twice the digits, if the difference is a multiple of 7, 7 can be the original number divisible. If the difference is too large or mental arithmetic easy to see whether a multiple of 7, it is necessary to continue the above "censored, times larger, subtraction, posterior error" process, until the determined date clearly. For example, the process determines 133 whether a multiple of 7 as follows: 13-3 × 2 = 7, it is a multiple of 7, 133; and 6139, for example, determining whether multiple of 7 process as follows: 613-9 × 2 = 595, 59-5 × 2 = 49, it is a multiple of 6139, and so more than 7.
(8) If the end of a three-digit integer not divisible by 8, then the number is divisible by 8.
(9) If an integer number of divisible and can be, then this can be an integer divisible.
(10) If the last bit is an integer of 0, then this number can be divisible by 10.
(11) and an even-odd digit if the digits of an integer and the difference can be divisible by 11, then this number can be divisible by 11. A multiple of 11 test method can also be used above checks 7 "cut tail Law" processing! The only difference is the process: multiple not 2 but 1!
(12) If an integer divisible by 3 and 4, then the number can be divisible by 12.
(13) if a digit integer truncated, and then from the remaining numbers, plus four times the single digits, if the difference is a multiple of 13, the number of the original 13 can be divisible. If the difference is too large or mental arithmetic easy to see whether a multiple of 13, it is necessary to continue the above "censored, times the size of the sum, difference test" process, until the determined date clearly.
(14) if a digit integer truncated, and then from the remaining number, the digits of subtracting five times, if the difference is a multiple of 17, the number of the original 17 can be divisible. If the difference is too large or mental arithmetic easy to see whether a multiple of 17, it is necessary to continue the above "censored, times larger, subtraction, posterior error" process, until the determined date clearly.
(15) if a digit integer truncated, and then from the remaining numbers, plus twice the digits, if the difference is a multiple of 19, the number of the original 19 can be divisible. If the difference is too big or mental arithmetic easy to see whether a multiple of 19, you need to continue the above "censored, times the size of the sum, experience poor" process, until you can clearly determine so far.
(16) If the end of a three integer of 3 times the previous interval be a difference in the number of 17 is divisible, then this number can be divisible by 17.
(17) If the end of the three preceding an integer of 7-fold difference compartment 19 can be divisible, then this number can be divisible by 19.
(18) if the last four integer with a 5-fold difference in the number of the front compartment 23 can be (or 29) is divisible, then this number can be divided by 23
7,11,13 divisible (19) to be wherein is the same: at the end of this three-digit number and the difference between the end of the previous three digit number of the number (turn OK) 7,11,13 be divisible. This number can be divisible 7,11,13.
For example: 1,005,928
Last three digits: 928, before the end of three: 10051005-928 = 77
since. 7 | 77, so. 7 | 1005928
Shank method:
remove the last one, minus its two times, the resulting number of look You can divisible by 7.
Such as: 42 (7)
--14
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2 (8)
- 16
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- 1 (4) ---14 be divisible by 14, it can be divisible by 7 427
cuts off the last one, the last bit plus five times , it may be determined.
Example: 200 (9)
+ 45
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24 (5)
+ 25
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4 (9) --- 49 is a multiple of 7, which can be divisible by 7 some Analyzing 2009
+ 45
--------
49
Reproduced in: https: //www.cnblogs.com/MichaelGuan/archive/2010/10/06/1844857.html