Test the divisibility of each of the following numbers by 8 :
(i) 6132 (ii) 7304 (iii) 59321 (iv) 66664 (v) 44444 (vi) 154360 (vii) 998818 (viii) 265472 (ix) 7350162

Answer

To test the divisibility of each of the given numbers by 8, we will follow the divisibility rule for 8, which states that if the number formed by the last three digits of a number is divisible by 8, then the entire number is also divisible by 8.

Let's go through each number step by step:

### Step-by-Step Solution:

1. **Number: 6132**
- Last three digits: **132**
- Check divisibility: \( 132 \div 8 = 16.5 \) (not divisible)
- Conclusion: **6132 is not divisible by 8.**

2. **Number: 7304**
- Last three digits: **304**
- Check divisibility: \( 304 \div 8 = 38 \) (divisible)
- Conclusion: **7304 is divisible by 8.**

3. **Number: 59321**
- Last three digits: **321**
- Check divisibility: \( 321 \div 8 = 40.125 \) (not divisible)
- Conclusion: **59321 is not divisible by 8.**

4. **Number: 66664**
- Last three digits: **664**
- Check divisibility: \( 664 \div 8 = 83 \) (divisible)
- Conclusion: **66664 is divisible by 8.**

5. **Number: 44444**
- Last three digits: **444**
- Check divisibility: \( 444 \div 8 = 55.5 \) (not divisible)
- Conclusion: **44444 is not divisible by 8.**

6. **Number: 154360**
- Last three digits: **360**
- Check divisibility: \( 360 \div 8 = 45 \) (divisible)
- Conclusion: **154360 is divisible by 8.**

7. **Number: 998818**
- Last three digits: **818**
- Check divisibility: \( 818 \div 8 = 102.25 \) (not divisible)
- Conclusion: **998818 is not divisible by 8.**

8. **Number: 265472**
- Last three digits: **472**
- Check divisibility: \( 472 \div 8 = 59 \) (divisible)
- Conclusion: **265472 is divisible by 8.**

9. **Number: 7350162**
- Last three digits: **162**
- Check divisibility: \( 162 \div 8 = 20.25 \) (not divisible)
- Conclusion: **7350162 is not divisible by 8.**

### Summary of Results:
- 6132: Not divisible by 8
- 7304: Divisible by 8
- 59321: Not divisible by 8
- 66664: Divisible by 8
- 44444: Not divisible by 8
- 154360: Divisible by 8
- 998818: Not divisible by 8
- 265472: Divisible by 8
- 7350162: Not divisible by 8