If 24a5 is a multiple of 3 i.e. divisible by 3, find the value of digit a.

Answer

To find the value of the digit \( a \) in the number \( 24a5 \) such that it is a multiple of 3, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Rule for Divisibility by 3**: A number is divisible by 3 if the sum of its digits is divisible by 3.

2. **Identify the Digits in the Number**: The digits of the number \( 24a5 \) are \( 2, 4, a, \) and \( 5 \).

3. **Calculate the Sum of the Known Digits**:
\[ 2 + 4 + 5 = 11 \]
So, the sum of the digits including \( a \) will be:
\[ 11 + a \]

4. **Set Up the Condition for Divisibility**: We need \( 11 + a \) to be divisible by 3.

5. **Check Possible Values of \( a \)**: Since \( a \) is a digit, it can take values from 0 to 9. We will check each value of \( a \) to see if \( 11 + a \) is divisible by 3.

- For \( a = 0 \): \( 11 + 0 = 11 \) (not divisible by 3)
- For \( a = 1 \): \( 11 + 1 = 12 \) (divisible by 3)
- For \( a = 2 \): \( 11 + 2 = 13 \) (not divisible by 3)
- For \( a = 3 \): \( 11 + 3 = 14 \) (not divisible by 3)
- For \( a = 4 \): \( 11 + 4 = 15 \) (divisible by 3)
- For \( a = 5 \): \( 11 + 5 = 16 \) (not divisible by 3)
- For \( a = 6 \): \( 11 + 6 = 17 \) (not divisible by 3)
- For \( a = 7 \): \( 11 + 7 = 18 \) (divisible by 3)
- For \( a = 8 \): \( 11 + 8 = 19 \) (not divisible by 3)
- For \( a = 9 \): \( 11 + 9 = 20 \) (not divisible by 3)

6. **List the Valid Values of \( a \)**: The values of \( a \) that make \( 11 + a \) divisible by 3 are:
- \( a = 1 \)
- \( a = 4 \)
- \( a = 7 \)

### Conclusion
The possible values of \( a \) that make \( 24a5 \) a multiple of 3 are \( 1, 4, \) and \( 7 \).