Which of the following numbers are divisible by 6?
(i) 53022 `" "` (ii) 751024

Answer

To determine which of the given numbers are divisible by 6, we need to apply the divisibility rules for both 2 and 3, since a number is divisible by 6 if it is divisible by both of these numbers.

### Step-by-Step Solution:

**Step 1: Check if 53022 is divisible by 2.**
- A number is divisible by 2 if its last digit is even.
- The last digit of 53022 is 2, which is even.
- Therefore, **53022 is divisible by 2.**

**Step 2: Check if 53022 is divisible by 3.**
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- The digits of 53022 are 5, 3, 0, 2, and 2.
- Calculate the sum:
- \(5 + 3 + 0 + 2 + 2 = 12\)
- Now check if 12 is divisible by 3:
- \(12 \div 3 = 4\) (which is a whole number)
- Therefore, **53022 is divisible by 3.**

**Step 3: Conclusion for 53022.**
- Since 53022 is divisible by both 2 and 3, it is also divisible by 6.

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**Step 4: Check if 751024 is divisible by 2.**
- The last digit of 751024 is 4, which is even.
- Therefore, **751024 is divisible by 2.**

**Step 5: Check if 751024 is divisible by 3.**
- The digits of 751024 are 7, 5, 1, 0, 2, and 4.
- Calculate the sum:
- \(7 + 5 + 1 + 0 + 2 + 4 = 19\)
- Now check if 19 is divisible by 3:
- \(19 \div 3 = 6.33\) (not a whole number)
- Therefore, **751024 is not divisible by 3.**

**Step 6: Conclusion for 751024.**
- Since 751024 is not divisible by 3, it cannot be divisible by 6.

### Final Answer:
- **53022 is divisible by 6.**
- **751024 is not divisible by 6.**

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