Can you explain the characteristics that can be divided by 7, 11, 13 Thank you very much~ OK, I'll add! For example, let's be more detailed! I'll be home!

Can you explain the characteristics that can be divided by 7, 11, 13 Thank you very much~ OK, I'll add! For example, let's be more detailed! I'll be home!

The difference between the sum of odd carry and even carry can be divided by 7, 11, or 13
　　7*11*13=1001
The difference of 1001 is 0
The characteristic of a number divisible by 7, 11 and 13 is that the difference (or vice versa) between the number composed by the last three digits of the number and the number composed by the number before the last three digits can be divisible by 7, 11 and 13
　　A=an·10n＋… +a3·103+a2·102＋a1·10+a0,
Let n be the number composed of the last three digits and m be the number composed of the numbers before the last three digits
　　N＝a2·102+a1·10＋a0,
　　M＝an·10n－8＋an-1·10n－4＋… ＋a3.
So a = m · 1000 + n = (m · 1000 + m) + (n-m)
　　＝M（1000+1）+N—M
If n > m, then
　　A=1001M＋（N-M）；
If n < m, then
　　A=1001M-（M-N）.
In the above two formulas, 1001 can be divisible by 7, 11 and 13, so the first term 1001m can also be divisible by 7, 11 and 13. Therefore, the characteristic of a divisible by 7, 11 and 13 is that (n-m) or (m-n) can be divisible by 7, 11 and 13. The number divisible by 11 has another characteristic: the difference (or vice versa) between the sum of the odd digits and the sum of the even digits can be divisible by 11
　　72358=7×(9999＋1）＋2×（1001—1）＋3
　　×（99＋1）＋5×（11—1）＋8
　　=（7×9999＋2×1001＋3×99＋5×11）
　　+[（7+3+8)-（2＋5)],
In the last formula above, the first addend can be divided by 11, so whether 72538 can be divided by 11 depends on whether the second addend can be divided by 11
　　（7＋3 ＋8）-（2＋5）=11,
Of course, it can be divided by 11, so 11 | 72358