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Which is the largest 4-digit number that can be exactly divisible by 66?
- a)9987
- b)9912
- c)9913
- d)9966
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Which is the largest 4-digit number that can be exactly divisible by 6...
The largest four-digit number is = 9999, and on dividing it with 66, we will get 33 as the remainder.
So, the largest 4-digit number divided by 66 = 9999 - 33 = 9966
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Community Answer
Which is the largest 4-digit number that can be exactly divisible by 6...
Explanation:
Finding the largest 4-digit number divisible by 66:
To find the largest 4-digit number that is exactly divisible by 66, we need to start by considering the highest 4-digit number, which is 9999.
Divisibility rule for 66:
- A number is divisible by 66 if it is divisible by both 6 and 11.
Finding the divisibility by 6:
- The sum of the digits of 9999 is 9+9+9+9 = 36, which is divisible by 6. Therefore, 9999 is divisible by 6.
Finding the divisibility by 11:
- Alternating the sum of the digits of 9999, we get (9-9) + (9-9) = 0. Since the result is 0, 9999 is divisible by 11.
Conclusion:
- Since 9999 is divisible by both 6 and 11, it is divisible by 66.
Checking the next highest number:
- The next highest 4-digit number is 9998, which is not divisible by 66 as it does not meet the divisibility criteria for both 6 and 11.
Therefore, the largest 4-digit number divisible by 66 is:
- 9966 (Option D)
Final Answer:
- The largest 4-digit number that can be exactly divisible by 66 is 9966.
Finding the largest 4-digit number divisible by 66:
To find the largest 4-digit number that is exactly divisible by 66, we need to start by considering the highest 4-digit number, which is 9999.
Divisibility rule for 66:
- A number is divisible by 66 if it is divisible by both 6 and 11.
Finding the divisibility by 6:
- The sum of the digits of 9999 is 9+9+9+9 = 36, which is divisible by 6. Therefore, 9999 is divisible by 6.
Finding the divisibility by 11:
- Alternating the sum of the digits of 9999, we get (9-9) + (9-9) = 0. Since the result is 0, 9999 is divisible by 11.
Conclusion:
- Since 9999 is divisible by both 6 and 11, it is divisible by 66.
Checking the next highest number:
- The next highest 4-digit number is 9998, which is not divisible by 66 as it does not meet the divisibility criteria for both 6 and 11.
Therefore, the largest 4-digit number divisible by 66 is:
- 9966 (Option D)
Final Answer:
- The largest 4-digit number that can be exactly divisible by 66 is 9966.
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