Which of the following numbers are divisible by 3?
(i) 754206 `" "` (ii)8537014

Answer

To determine whether the given numbers are divisible by 3, we will use the rule that states a number is divisible by 3 if the sum of its digits is divisible by 3. Let's solve the problem step by step.

### Step 1: Check the first number, 754206.

1. **Identify the digits**: The digits of the number 754206 are 7, 5, 4, 2, 0, and 6.
2. **Calculate the sum of the digits**:
- \( 7 + 5 = 12 \)
- \( 12 + 4 = 16 \)
- \( 16 + 2 = 18 \)
- \( 18 + 0 = 18 \)
- \( 18 + 6 = 24 \)

3. **Check if the sum is divisible by 3**:
- The sum of the digits is 24.
- Since \( 24 \div 3 = 8 \) (which is a whole number), 24 is divisible by 3.

**Conclusion for 754206**: The number 754206 is divisible by 3.

### Step 2: Check the second number, 8537014.

1. **Identify the digits**: The digits of the number 8537014 are 8, 5, 3, 7, 0, 1, and 4.
2. **Calculate the sum of the digits**:
- \( 8 + 5 = 13 \)
- \( 13 + 3 = 16 \)
- \( 16 + 7 = 23 \)
- \( 23 + 0 = 23 \)
- \( 23 + 1 = 24 \)
- \( 24 + 4 = 28 \)

3. **Check if the sum is divisible by 3**:
- The sum of the digits is 28.
- Since \( 28 \div 3 \) does not result in a whole number (it equals approximately 9.33), 28 is not divisible by 3.

**Conclusion for 8537014**: The number 8537014 is not divisible by 3.

### Final Results:
- **754206**: Divisible by 3
- **8537014**: Not divisible by 3

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