Answer: Divisor = 9, quotient = 51
Let the divisor be \(x\); quotient \(= 5x + 6\). Dividend = divisor × quotient + remainder:
\[x(5x + 6) + 1 = 460\]\[5x^2 + 6x - 459 = 0\]\(b^2 - 4ac = 36 + 9180 = 9216 = 96^2\)
\[x = \frac{-6 \pm 96}{10}\]\(x = 9\) (the other value \(-10.2\) is not natural). Quotient \(= 5(9) + 6 = 51\). Check: \(9 \times 51 + 1 = 460\).