It is proved that any three digit can be divided by 7,11,13 at the same time

It is proved that any three digit can be divided by 7,11,13 at the same time

Any three digit number written twice must be a multiple of 1001, and 1001 = 7 * 11 * 13, so it must be divisible by 7, 11 and 13 at the same time, such as 123123 = 123 * 7 * 11 * 13

If six digit abacbc is known, try to judge whether six digit can be divided by 7, 11 and 13, and explain the reason

Obviously, six digit abacbc can't be divisible by 7,11,13. As the first floor said: abacbc = 101000a + 10010b + 101c, these three numbers are not necessarily related. Using the special value method, we can also explain that, for example, 414515,7,11,13 can't be divisible. If it's six digit abacbc, it can be divisible by 7,11,13