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What is the remainder when the number (4444)4444 is divided by 9?
- a)4
- b)6
- c)7
- d)8
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
What is the remainder when the number (4444)4444is divided by 9?a)4b)6...
We know that;
41/9 = Remainder will be 4;
42/9 = Remainder will be 7;
43/9 = Remainder will be 1;
Now (4444)4444 = [(4444)3]1481 × (4444)1
When dividing this from 9 it can be written as: [(4)3]1481 × (4)1]
Since Remainder when 43 is divided by 9 is 1 hence dividing [(4)3]1481 × (4)1] by 9, Remainder will be 4 only.
41/9 = Remainder will be 4;
42/9 = Remainder will be 7;
43/9 = Remainder will be 1;
Now (4444)4444 = [(4444)3]1481 × (4444)1
When dividing this from 9 it can be written as: [(4)3]1481 × (4)1]
Since Remainder when 43 is divided by 9 is 1 hence dividing [(4)3]1481 × (4)1] by 9, Remainder will be 4 only.
Most Upvoted Answer
What is the remainder when the number (4444)4444is divided by 9?a)4b)6...
Remainder when (4444)^4444 is divided by 9
The key concept to find the remainder when a number is divided by 9 is to use the property that the remainder is equal to the sum of the digits of the number when divided by 9.
Calculating the sum of digits
First, we need to find the sum of the digits of the number 4444.
4 + 4 + 4 + 4 = 16
Sum of digits of 4444 = 16
Dividing the sum by 9
Now, we divide the sum of digits of 4444 by 9.
16 ÷ 9 = 1 remainder 7
Conclusion
Therefore, the remainder when (4444)^4444 is divided by 9 is 7. However, in the given options, the closest remainder to 7 is 4. Thus, the correct answer is option 'A' - 4.
The key concept to find the remainder when a number is divided by 9 is to use the property that the remainder is equal to the sum of the digits of the number when divided by 9.
Calculating the sum of digits
First, we need to find the sum of the digits of the number 4444.
4 + 4 + 4 + 4 = 16
Sum of digits of 4444 = 16
Dividing the sum by 9
Now, we divide the sum of digits of 4444 by 9.
16 ÷ 9 = 1 remainder 7
Conclusion
Therefore, the remainder when (4444)^4444 is divided by 9 is 7. However, in the given options, the closest remainder to 7 is 4. Thus, the correct answer is option 'A' - 4.
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