Using test of divisibility, find if 543368 is divisible by 12 or not

Answer

To determine if the number 543368 is divisible by 12, we need to check if it is divisible by both 3 and 4, as per the test of divisibility for 12.

### Step-by-Step Solution:

1. **Check Divisibility by 3**:
- To check if a number is divisible by 3, we need to sum all its digits and see if the result is divisible by 3.
- The digits of 543368 are: 5, 4, 3, 3, 6, and 8.
- Now, we add these digits together:
- \( 5 + 4 = 9 \)
- \( 9 + 3 = 12 \)
- \( 12 + 3 = 15 \)
- \( 15 + 6 = 21 \)
- \( 21 + 8 = 29 \)
- The sum of the digits is 29.

2. **Check if 29 is Divisible by 3**:
- Now, we check if 29 is divisible by 3.
- Since \( 29 \div 3 = 9.67 \) (not a whole number), 29 is not divisible by 3.

3. **Conclusion on Divisibility by 3**:
- Since 543368 is not divisible by 3, it cannot be divisible by 12.

4. **Check Divisibility by 4** (though unnecessary since we already know it's not divisible by 12):
- To check if a number is divisible by 4, we look at the last two digits of the number.
- The last two digits of 543368 are 68.
- Now, we check if 68 is divisible by 4:
- \( 68 \div 4 = 17 \) (which is a whole number).
- Therefore, 68 is divisible by 4.

5. **Final Conclusion**:
- Since 543368 is not divisible by 3, it is not divisible by 12, regardless of its divisibility by 4.

### Answer:
543368 is not divisible by 12.

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