The number 12375 is divisible by :

Options

A. 3,11 and 9
B. 3 and 11 only
C. 11 and 9 only
D. 3 and 9 only

Answer

To determine the divisibility of the number 12375 by 3, 9, and 11, we will use the respective divisibility rules for each of these numbers.

### Step-by-step Solution:

**Step 1: Check divisibility by 3**
- **Rule:** A number is divisible by 3 if the sum of its digits is divisible by 3.
- **Calculation:**
- Sum of the digits of 12375:
\( 1 + 2 + 3 + 7 + 5 = 18 \)
- **Check:**
- Since 18 is divisible by 3 (18 ÷ 3 = 6), the number 12375 is divisible by 3.

**Step 2: Check divisibility by 9**
- **Rule:** A number is divisible by 9 if the sum of its digits is divisible by 9.
- **Check:**
- We already calculated the sum of the digits as 18.
- Since 18 is divisible by 9 (18 ÷ 9 = 2), the number 12375 is also divisible by 9.

**Step 3: Check divisibility by 11**
- **Rule:** A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is either 0 or a multiple of 11.
- **Calculation:**
- Odd position digits: 1 (1st), 3 (3rd), 5 (5th) → Sum = \( 1 + 3 + 5 = 9 \)
- Even position digits: 2 (2nd), 7 (4th) → Sum = \( 2 + 7 = 9 \)
- **Check:**
- Difference = \( |9 - 9| = 0 \)
- Since the difference is 0, the number 12375 is divisible by 11.

### Conclusion:
The number 12375 is divisible by 3, 9, and 11.

### Final Answer:
The correct option is: **3, 11, and 9.**

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