If the sum of your numbers can be divided by 9, then the number can be divided by 9. Please explain the reason and give a characteristic that three digits can be divided by 7

If the sum of your numbers can be divided by 9, then the number can be divided by 9. Please explain the reason and give a characteristic that three digits can be divided by 7

If the hundred of three digits is a, the ten digits are B, and each digit is C, then this number can be expressed as 100A + 10B + C
Can get
100A+10B+C=99A+9B+(A+B+C)
Because a + B + C is divisible by 9
The difference between the last three digits of the number and the number before the last three digits (or vice versa) can be divided by 7, 11 and 13. The number can be divided by 7, 11 and 13