Characteristics of numbers divisible by 7,11,13,17 Write as much as you have

Characteristics of numbers divisible by 7,11,13,17 Write as much as you have

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If the number of one digit of an integer is truncated, and then two times of the number of one digit is subtracted from the remaining number, if the difference is a multiple of 7, then the original number can be divided by 7. If the difference is too large or it is difficult to see whether it is a multiple of 7 by mental arithmetic, we need to continue the above process of "truncation, multiplication, subtraction and difference checking" until we can make a clear judgment. For example, the process of judging whether 133 is a multiple of 7 is as follows: 13-3 × 2 = 7, So 133 is a multiple of 7; for example, the process of judging whether 6139 is a multiple of 7 is as follows: 613-9 × 2 = 595, 59-5 × 2 = 49, so 6139 is a multiple of 7, and so on
If the difference between the sum of odd digits and the sum of even digits of an integer can be divided by 11, then the number can be divided by 11. The multiple test method of 11 can also be processed by the "tail cutting method" of check 7. The only difference in the process is that the multiple is not 2, but 1!
If the number of one digit of an integer is truncated, and then four times of the number of one digit is added to the remaining number, if the difference is a multiple of 13, then the original number can be divided by 13. If the difference is too large or it is difficult to see whether it is a multiple of 13 by mental arithmetic, we need to continue the above process of "truncation, multiplication, addition and difference checking" until we can make a clear judgment
If the difference between the last three digits of an integer and the preceding number of 7 times can be divided by 19, then the number can be divided by 19