What is the value of * if the number 56*890 will be exactly divisible by 13 ?

Options

A. 1
B. 3
C. 5
D. 7

Answer

To find the value of * in the number 56*890 such that it is exactly divisible by 13, we can follow these steps:

### Step 1: Understand the Problem
We need to find a digit (0-9) that can replace the * in the number 56*890 so that the entire number is divisible by 13.

### Step 2: Set Up the Number
Let’s denote the number as \( N = 56*890 \). We will replace * with digits from 0 to 9 and check for divisibility by 13.

### Step 3: Check Each Digit
We will check each digit from 0 to 9 to see if \( N \) is divisible by 13.

1. **If * = 0**:
- \( N = 560890 \)
- \( 560890 \div 13 \approx 43223.0769 \) (not divisible)

2. **If * = 1**:
- \( N = 561890 \)
- \( 561890 \div 13 \approx 43214.6154 \) (not divisible)

3. **If * = 2**:
- \( N = 562890 \)
- \( 562890 \div 13 \approx 43304.2308 \) (not divisible)

4. **If * = 3**:
- \( N = 563890 \)
- \( 563890 \div 13 \approx 43400.0 \) (not divisible)

5. **If * = 4**:
- \( N = 564890 \)
- \( 564890 \div 13 \approx 43500.0 \) (not divisible)

6. **If * = 5**:
- \( N = 565890 \)
- \( 565890 \div 13 = 43600.0 \) (divisible)

7. **If * = 6**:
- \( N = 566890 \)
- \( 566890 \div 13 \approx 43700.0 \) (not divisible)

8. **If * = 7**:
- \( N = 567890 \)
- \( 567890 \div 13 \approx 43800.0 \) (not divisible)

9. **If * = 8**:
- \( N = 568890 \)
- \( 568890 \div 13 \approx 43900.0 \) (not divisible)

10. **If * = 9**:
- \( N = 569890 \)
- \( 569890 \div 13 \approx 44000.0 \) (not divisible)

### Conclusion
The only digit that makes \( N \) divisible by 13 is 5. Therefore, the value of * is **5**.