Which of the following numbers is divisible by both 4 and 9?

Options

A. 2368
B. 2736
C. 3954
D. 3814

Answer

To determine which of the given numbers is divisible by both 4 and 9, we will follow these steps:

### Step 1: Understand the divisibility rules
- A number is divisible by **4** if the last two digits of the number form a number that is divisible by 4.
- A number is divisible by **9** if the sum of its digits is divisible by 9.

### Step 2: List the options
We have the following options:
1. Option 1: 2, 3, 6, 8
2. Option 2: 2, 7, 3, 6
3. Option 3: 3, 9, 5, 4
4. Option 4: 3, 8, 1, 4

### Step 3: Check each option for divisibility by 4
- **Option 1 (2, 3, 6, 8)**: The last two digits are 6 and 8. 68 is divisible by 4.
- **Option 2 (2, 7, 3, 6)**: The last two digits are 3 and 6. 36 is divisible by 4.
- **Option 3 (3, 9, 5, 4)**: The last two digits are 5 and 4. 54 is not divisible by 4.
- **Option 4 (3, 8, 1, 4)**: The last two digits are 1 and 4. 14 is not divisible by 4.

### Step 4: Check the valid options for divisibility by 9
Now we will check the options that passed the divisibility test for 4:
- **Option 1 (2, 3, 6, 8)**: Sum of digits = 2 + 3 + 6 + 8 = 19. Not divisible by 9.
- **Option 2 (2, 7, 3, 6)**: Sum of digits = 2 + 7 + 3 + 6 = 18. Divisible by 9.

### Conclusion
The only option that is divisible by both 4 and 9 is **Option 2: 2, 7, 3, 6**.