Find which of the following numbers are divsible by 3 :
(i) 261 (ii) 777
(iii) 6657 (iv) 2574

Options

A. `(i)` and `(ii)`
B. `(iii)` and `(iv)`
C. All
D. None of these

Answer

To determine which of 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 check each number step by step.

### Step 1: Check the number 261
1. **Sum the digits**:
- \(2 + 6 + 1 = 9\)
2. **Check divisibility**:
- Since \(9\) is divisible by \(3\) (as \(3 \times 3 = 9\)), we conclude that **261 is divisible by 3**.

### Step 2: Check the number 777
1. **Sum the digits**:
- \(7 + 7 + 7 = 21\)
2. **Check divisibility**:
- Since \(21\) is divisible by \(3\) (as \(3 \times 7 = 21\)), we conclude that **777 is divisible by 3**.

### Step 3: Check the number 6657
1. **Sum the digits**:
- \(6 + 6 + 5 + 7 = 24\)
2. **Check divisibility**:
- Since \(24\) is divisible by \(3\) (as \(3 \times 8 = 24\)), we conclude that **6657 is divisible by 3**.

### Step 4: Check the number 2574
1. **Sum the digits**:
- \(2 + 5 + 7 + 4 = 18\)
2. **Check divisibility**:
- Since \(18\) is divisible by \(3\) (as \(3 \times 6 = 18\)), we conclude that **2574 is divisible by 3**.

### Final Conclusion:
All four numbers are divisible by 3:
- 261 is divisible by 3.
- 777 is divisible by 3.
- 6657 is divisible by 3.
- 2574 is divisible by 3.

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