Tail cutting, as the name implies, refers to the multiple of the number formed by the high digit of the number - the low digit (usually the last one).Cut is subtract;The tail is the number of the lower form.
The tail cutting method of integral division is to use the divisibility of the number obtained in the above way to judge the divisibility of the original number.
Some numbers have a specialto be divisible bySex.For example, the number that can be divided by 11 can be divided by 11.For example, 121, 12-1=11, 11 can be divided by 11, so 121 can.This method is good for 11, but not necessarily for others.(When a number is de tailed by one time, it is actually a multiple of 11, and the remaining number is removed by the following zero (because no matter how many powers of 10 can be divided by 11). Therefore, if the remaining number can be divided by 11, it is enough to show that the original number can be divided by 11. It is also similar to use odd and even digits and difference to explain the reason)
Another example is that 13 is four times more tail (or nine times less tail), 17 is five times more tail (or twelve times more tail), and 19 is two times more tail (or seventeen times less tail)
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So what are the rules between them?
And, for example.Change one method(The German elementary school students' method, also known as the method of calculating the root number of multi digit numbers, is roughly like this: for example, 169 divided by 13 is equal to 13, 6+6+9=16, 1+3=4. Then 16 divided by four is equal to four. Moreover, the addition, subtraction, multiplication and division of integers greater than or equal to two digits all conform to this rule. Therefore, this method is most widely used to check whether the results of complex mixed operations are correct. In short, the method of changing one isIt refers to the operation of repeatedly summing the number on each bit of a number until it is reduced to a number less than 10. For example, 123156 uses the method of changing one: 1+2+3+4+5+6=21,2+1=3, then 123456 changes one to get the number 3But division must be converted into multiplication.)When dealing with the 13 multiples of the four times of the tail, we found that they had a regression: 26 still 26 (6 times 4 plus 2), 39 still 39, 52 changed to 13, 78 changed to 39... Then we found that the number of 8 and 11, etc. obtained by the change one method would turn into 26;Change one to 7, 10, 13 and so on, and you will get 13;Change one to get 12, 15, etc., and get 39.Then 8, 11;7，10，13……；12, 15...... Are respectively divided into equal difference series.
Later, someone put forward that the relevant information of 11 can also be explained as follows:
For an n-digit a, it is expressed as a=10 x+y, where y is the single digit of a, and x is the n-1 digit of a after removing the single digit y.(For example, if a is 121, y is 1, and x is 12.)
A=10 x+y=11x - (x-y), obviously, as long as x-y can be divided by 11, a can be divided by 11.(For example, if a is 121, y is 1, and x-y is 12-1=11)
This method can be popularized for such problems, such as 13 related proofs:
a=10x+y=13x+13y-3x-12y=13(x+y)-3(x+4y)；
Or a=10 x+y=13x-26y-3x+27y=13 (x-2y) - 3 (x-9y).
The above similar problems can be solved one by one
