How to determine whether a number can be divisible by 7

For example, the method for determining whether a number can be divisible by 7 is as follows: for example, if 344617 can be divisible by 7, 617-344 = 273,273 can be divisible by 7, so 344617 can be divisible by 7. For example, if 4241468 can be divisible by 7, 468-241 + 4 = 231 can be divisible by 7. So how can we prove this method when 4241468 can be divisible by 7? It is best to answer in Chinese. It is easy to use.

The technique is very simple. You only need 1001 = 7*11*13. Please take a look at the following.

You are more than a Chinese version ︰

Set a six-digit abcdef.
So,
Abcdef = 100000a + rjb + 1000c + 100d + 10E + F
= (100100a-100a) + (10010b-10B) + (1001c-C) + 100d + 10E + F
= (100100a + 10010b + 1001c) + (100d + 10E + F)-(100a + 10b + C)
= 7 * (14300a + 1430b + 143c) + (100d + 10E + F)-(100a + 10b + C)

The first parenthesis of the preceding formula is a multiple of 7. Therefore, to determine whether the six-digit abcdef can be fully divided by 7, see (100d + 10E + F)-(100a + 10b + C ),
That is, whether the difference between the first and second three digits def-ABC can be divided into seven.


But is this method applicable to single-digit numbers? Similar methods.
Set another seven-digit abcdefg.
Abcdefg = 000000a + 100000b + 0000c + 1000d + 100e + 10f + G
= (1001000a-1000a) + (100100b-100b) + (10010c-10C) + (1001d-D) + 100e + 10f + G
= (1001000a + 100100b + 10010c + 1001d) + (100e + 10f + G)-(1000a + 100b + 10C + D)
= 7 * (143000a + 14300b + 1430c + 143d) + (100e + 10f + G)-(1000a + 100b + 10C + D)

Similarly, the method to determine whether the six-digit abcdefg can be fully divided by 7 depends on whether the difference between the four-digit front side and the three-digit back-end EFG-ABCD can be fully divided by 7.


To sum up, the method to determine whether a number can be divisible by 7 is ︰
Whether the difference between the three digits behind and the front digit can be divisible by seven.