Question

5304a is five digit number divisible by 6. List all the possible values of a, and show your steps.

Answer 1

To determine the values of a, we need to find the values that make 5304a divisible by 6.

A number is divisible by 6 if it is divisible by both 2 and 3.

To be divisible by 2, the last digit (a) of the number must be even.

To be divisible by 3, the sum of the digits of the number must be divisible by 3.

Let's calculate the sum of the digits of 5304a for each possible value of a:

For a = 0:
5 + 3 + 0 + 4 + 0 = 12
12 is divisible by 3, so 53040 is divisible by 6.

For a = 2:
5 + 3 + 0 + 4 + 2 = 14
14 is not divisible by 3, so 53042 is not divisible by 6.

For a = 4:
5 + 3 + 0 + 4 + 4 = 16
16 is not divisible by 3, so 53044 is not divisible by 6.

For a = 6:
5 + 3 + 0 + 4 + 6 = 18
18 is divisible by 3, so 53046 is divisible by 6.

For a = 8:
5 + 3 + 0 + 4 + 8 = 20
20 is not divisible by 3, so 53048 is not divisible by 6.

Therefore, the possible values of a are 0, 6.