2) If the sum of the numbers of an integer is divisible by 3, then the integer can be divisible by 3.
3) If the last two digits of an integer are divisible by 4, then this number can be divisible by 4.
4) If the last digit of an integer is 0 or 5, then this number can be divisible by 5.
5) If an integer is divisible by 2 and 3, it is divisible by 6.
6) If one digit of an integer is truncated, 2 times of the digit is subtracted from the remaining number. If the difference is a multiple of 7, the original number can be divisible by 7. If the difference is too big or it is difficult to see whether it is a multiple of 7 in mental arithmetic, we should continue the above-mentioned process of "rounding, multiplication, subtraction and difference test" 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 another example, the process of judging whether 6 139 is a multiple of 7 is as follows: 6 13-9× 2 = 595, 59-5× 2 = 49, so 6 139 is a multiple of 7, and so on.
7) If the last three digits of an integer are divisible by 8, then the number can be divisible by 8.
8) If the sum of the numbers of an integer is divisible by 9, then the integer can be divisible by 9.
9) If the last digit of an integer is 0, then this number can be divisible by 10.
10) If the difference between the sum of odd digits and the sum of even digits of an integer can be divisible by 1 1, then this number can be divisible by 1 1. 1 1 can also be processed by the "tail-cutting method" in the above inspection 7! The only difference in the process is that the multiple is 1 instead of 2!
1 1) If an integer is divisible by 3 and 4, then this number is divisible by 12.
12) If the single digits of an integer are truncated and then four times the single digits are added to the remainder, if the difference is a multiple of 13, the original number can be divisible by 13. If the difference is too big or it is difficult to see whether it is a multiple of 13 in mental arithmetic, it is necessary to continue the above-mentioned process of "truncation, multiplication, addition and difference test" until it can be clearly judged.
13) If the single digit of an integer is truncated, and then the remainder is subtracted by 5 times of the single digit, if the difference is a multiple of 17, then the original number can be divisible by 17. If the difference is too large or it is difficult to see whether it is a multiple of 17 in mental arithmetic, it is necessary to continue the above-mentioned process of "rounding, multiplication, subtraction and difference test" until it can be clearly judged.
14) If the single digit of an integer is truncated, and then twice the single digit is added to the remainder, if the difference is a multiple of 19, then the original number can be divisible by 19. If the difference is too big or it is difficult to see whether it is a multiple of 19 in mental arithmetic, it is necessary to continue the above-mentioned process of "truncation, multiplication, addition and difference test" until it can be clearly judged.
15) If the difference between the last three digits of an integer and the previous quantile is divisible by 17, then this number can be divisible by 17.
16) If the difference between the last three digits of an integer and seven times the previous quantile is divisible by 19, then this number can be divisible by 19.
17) If the difference between the last four digits of an integer and the first five times of the separated number can be divisible by 23 (or 29), then this number can be divisible by 23.