Test the divisibility of the following numbers by 6 : (i) 2070 (ii) 46523 (iii) 71232 (iv) 934706 (v) 251780 (vi) 872536

Answer

To determine if the given numbers are divisible by 6, we need to check if they are divisible by both 2 and 3. Here’s how we can do that step-by-step for each number:

### Step-by-Step Solution:

**(i) 2070**
1. **Check divisibility by 2:**
- The unit digit is 0 (which is even).
- Therefore, 2070 is divisible by 2.

2. **Check divisibility by 3:**
- Sum of the digits: 2 + 0 + 7 + 0 = 9.
- 9 is divisible by 3 (3 × 3 = 9).
- Therefore, 2070 is divisible by 3.

3. **Conclusion:**
- Since 2070 is divisible by both 2 and 3, it is divisible by 6.

**(ii) 46523**
1. **Check divisibility by 2:**
- The unit digit is 3 (which is odd).
- Therefore, 46523 is not divisible by 2.

2. **Conclusion:**
- Since 46523 is not divisible by 2, it cannot be divisible by 6.

**(iii) 71232**
1. **Check divisibility by 2:**
- The unit digit is 2 (which is even).
- Therefore, 71232 is divisible by 2.

2. **Check divisibility by 3:**
- Sum of the digits: 7 + 1 + 2 + 3 + 2 = 15.
- 15 is divisible by 3 (3 × 5 = 15).
- Therefore, 71232 is divisible by 3.

3. **Conclusion:**
- Since 71232 is divisible by both 2 and 3, it is divisible by 6.

**(iv) 934706**
1. **Check divisibility by 2:**
- The unit digit is 6 (which is even).
- Therefore, 934706 is divisible by 2.

2. **Check divisibility by 3:**
- Sum of the digits: 9 + 3 + 4 + 7 + 0 + 6 = 29.
- 29 is not divisible by 3.

3. **Conclusion:**
- Since 934706 is not divisible by 3, it cannot be divisible by 6.

**(v) 251780**
1. **Check divisibility by 2:**
- The unit digit is 0 (which is even).
- Therefore, 251780 is divisible by 2.

2. **Check divisibility by 3:**
- Sum of the digits: 2 + 5 + 1 + 7 + 8 + 0 = 23.
- 23 is not divisible by 3.

3. **Conclusion:**
- Since 251780 is not divisible by 3, it cannot be divisible by 6.

**(vi) 872536**
1. **Check divisibility by 2:**
- The unit digit is 6 (which is even).
- Therefore, 872536 is divisible by 2.

2. **Check divisibility by 3:**
- Sum of the digits: 8 + 7 + 2 + 5 + 3 + 6 = 31.
- 31 is not divisible by 3.

3. **Conclusion:**
- Since 872536 is not divisible by 3, it cannot be divisible by 6.

### Final Results:
- 2070: Divisible by 6
- 46523: Not divisible by 6
- 71232: Divisible by 6
- 934706: Not divisible by 6
- 251780: Not divisible by 6
- 872536: Not divisible by 6