Question
Download Solution PDFA number when divided by 7 leaves remainder of 4. If the square of the same number is divided by 7, then what is the remainder?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A number when divided by 7 leaves a remainder of 4.
Concept used:
Dividend = Divisor × Quotient + Remainder
Calculation:
Let the number and quotient be N and D respectively.
According to the question,
N = 7D + 4
⇒ N2 = (7D + 4)2
⇒ N2 = 49D2 + 56D + 16
⇒ N2 = 7(7D2 + 8D + 2) + 2
So, 7(7D2 + 8D + 2) is completely divisible by 7.
Now, the remainder is 2.
∴ The remainder is 2.
Last updated on Jul 21, 2025
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