The number ends with a 0, 2, 4, 6, or 8.
For example, 372, the sum of the digits is 3 + 7 + 2 = 9. 9 is divisible by 3 and 9, therefor, 372 is divisible by 3 and 9.
It is also divisible by 6. to prove divisibility by 6, we check if it is divisible by 3. If it is, we also check if it is divisible by 2. If the number is divisible by 3 and 2, then it is divisible by 6.
For 2, we check if the last digit is divisible by 2.
for 4, we check if the last 2 digits are divisible by 4.
For 8, we check if the last 4 digits are divisible by 8.
(and yes, there is a pattern here that works for 16, 32, 64...
For example, 6534, we add 4+5 to get 9.
We then add 6+3 to get 9.
9-9=0. 6534 is evenly divisible by 11.