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A number, when divided by 16, leaves a remainder 4. When the square of the number is divided by 16, what will be the remainder?
- a)1
- b)2
- c)3
- d)0
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A number, when divided by 16, leaves a remainder 4. When the square of...
Let the number be = 16k + 4 (where k is positive integer.)
Square of the number = (16k + 4)2 = 256k2 + 16 + 128k
Now, we have to find the remainder when the above number is divided by 16.
We will see the reminder of each term when it is divided by 4.
Since 256k2 and 128k will give the remainder 0 and 16 will give the remainder 0 when divided by 4.
So the required remainder = 0 + 0 + 0 = 0
Most Upvoted Answer
A number, when divided by 16, leaves a remainder 4. When the square of...
Understanding the Problem
When a number is divided by 16 and leaves a remainder of 4, it can be expressed as:
- Number = 16k + 4, where k is an integer.
Finding the Square of the Number
To find the remainder when the square of this number is divided by 16, we first calculate the square:
- Square = (16k + 4)²
Now, we can expand this expression:
- Square = 256k² + 128k + 16
Simplifying the Expression
When we divide this expression by 16, we focus on the terms that affect the remainder:
- 256k² is divisible by 16, so it leaves a remainder of 0.
- 128k is also divisible by 16, leaving a remainder of 0.
- The term 16 leaves a remainder of 0.
Now, we need to consider just the constant term from our original number:
- Square = (16k + 4)² = 0 + 0 + 16 + 8 = 16 + 8 = 8
Calculating the Final Remainder
The important aspect is that when we look closely, we should only focus on the square of the remainder:
- Remainder of the original number = 4
- Now, squaring the remainder: 4² = 16.
When we divide 16 by 16, the remainder is:
- Remainder = 0.
Conclusion
Thus, when the square of the number is divided by 16, the remainder is:
- 0
Therefore, the correct answer is option 'D'.
When a number is divided by 16 and leaves a remainder of 4, it can be expressed as:
- Number = 16k + 4, where k is an integer.
Finding the Square of the Number
To find the remainder when the square of this number is divided by 16, we first calculate the square:
- Square = (16k + 4)²
Now, we can expand this expression:
- Square = 256k² + 128k + 16
Simplifying the Expression
When we divide this expression by 16, we focus on the terms that affect the remainder:
- 256k² is divisible by 16, so it leaves a remainder of 0.
- 128k is also divisible by 16, leaving a remainder of 0.
- The term 16 leaves a remainder of 0.
Now, we need to consider just the constant term from our original number:
- Square = (16k + 4)² = 0 + 0 + 16 + 8 = 16 + 8 = 8
Calculating the Final Remainder
The important aspect is that when we look closely, we should only focus on the square of the remainder:
- Remainder of the original number = 4
- Now, squaring the remainder: 4² = 16.
When we divide 16 by 16, the remainder is:
- Remainder = 0.
Conclusion
Thus, when the square of the number is divided by 16, the remainder is:
- 0
Therefore, the correct answer is option 'D'.
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A number, when divided by 16, leaves a remainder 4. When the square of the number is divided by 16, what will be the remainder?a)1b)2c)3d)0Correct answer is option 'D'. Can you explain this answer?
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