5304a is five digit number divisible by 6. List all the possible values of a.
In order for a five-digit number to be divisible by 6, it must be divisible by both 2 and 3.
For a number to be divisible by 2, the last digit must be even. Since a can take any digit from 0 to 9, the possible values of a that are even are 0, 2, 4, 6, 8.
For a number to be divisible by 3, the sum of its digits must be divisible by 3. Since the number is a five-digit number and a is one of its digits, the sum of its digits is 5a + the sum of the other four digits. The sum of the other four digits can range from 0 (if all four of them are 0) to 36 (if they are all 9). So, the sum of all five digits (including a) can range from 5a to 5a + 36.
For the sum of all five digits to be divisible by 3, the possible values of a must fall within the range of values for which the sum is divisible by 3.
The values of a that satisfy this condition are 0, 3, 6, and 9.
Therefore, the possible values of a are 0, 2, 3, 4, 6, 8, and 9.