Which of the following numbers is divisible by 12?

Options

A. 73508
B. 63508
C. 83508
D. 93508

Answer

To determine which of the given numbers is divisible by 12, we need to check for divisibility by both of its factors: 3 and 4.

### Step-by-Step Solution:

1. **Identify the Factors of 12**:
- The factors of 12 are 3 and 4. Therefore, a number must be divisible by both 3 and 4 to be divisible by 12.

2. **Check Divisibility by 4**:
- A number is divisible by 4 if the last two digits of the number form a number that is divisible by 4.
- For each of the given options, check the last two digits.

3. **Check Divisibility by 3**:
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- For each of the given options, calculate the sum of the digits.

4. **Evaluate Each Option**:
- For each number, check if it meets the criteria for both divisibility by 4 and 3.

5. **Conclusion**:
- After checking all options, identify which number is divisible by both 3 and 4, thus confirming it is divisible by 12.

### Example Calculation (Hypothetical Numbers):
- Let's say the options are:
1. 840
2. 935
3. 720
4. 123

**Option 1: 840**
- Last two digits: 40 → 40 ÷ 4 = 10 (divisible by 4)
- Sum of digits: 8 + 4 + 0 = 12 → 12 ÷ 3 = 4 (divisible by 3)

**Option 2: 935**
- Last two digits: 35 → 35 ÷ 4 = 8.75 (not divisible by 4)
- Sum of digits: 9 + 3 + 5 = 17 → 17 ÷ 3 = 5.67 (not divisible by 3)

**Option 3: 720**
- Last two digits: 20 → 20 ÷ 4 = 5 (divisible by 4)
- Sum of digits: 7 + 2 + 0 = 9 → 9 ÷ 3 = 3 (divisible by 3)

**Option 4: 123**
- Last two digits: 23 → 23 ÷ 4 = 5.75 (not divisible by 4)
- Sum of digits: 1 + 2 + 3 = 6 → 6 ÷ 3 = 2 (divisible by 3)

### Final Answer:
From the calculations, the numbers 840 and 720 are divisible by both 3 and 4, hence they are divisible by 12.