1. **Problem Statement:** Divide the hexadecimal number $\text{(13AF9)}_{16}$ by $\text{(9A)}_{16}$ and find the quotient and remainder. 2. **Convert divisor to decimal:** $$\text{(9A)}_{16} = 9 \times 16^1 + A \times 16^0 = 9 \times 16 + 10 = 144 + 10 = 154_{10}$$ 3. **Convert dividend to decimal for understanding:** $$\text{(13AF9)}_{16} = 1 \times 16^4 + 3 \times 16^3 + A \times 16^2 + F \times 16^1 + 9 \times 16^0$$ $$= 1 \times 65536 + 3 \times 4096 + 10 \times 256 + 15 \times 16 + 9 = 65536 + 12288 + 2560 + 240 + 9 = 80633_{10}$$ 4. **Perform division in decimal:** $$80633 \div 154 = 523 \text{ remainder } 5B_{16} \text{ (to be verified)}$$ 5. **Convert quotient back to hexadecimal:** $$523_{10} = 2 \times 256 + 0 \times 16 + 11 = \text{(20B)}_{16}$$ 6. **Calculate remainder in decimal:** $$80633 - 154 \times 523 = 80633 - 80542 = 91_{10}$$ 7. **Convert remainder to hexadecimal:** $$91_{10} = 5 \times 16 + 11 = \text{(5B)}_{16}$$ 8. **Conclusion:** $$\frac{\text{(13AF9)}_{16}}{\text{(9A)}_{16}} = \text{(20B)}_{16} \text{ remainder } \text{(5B)}_{16}$$ Hexadecimal division follows the same principles as decimal division but uses base 16 arithmetic. **Final answer:** Quotient = $\text{(20B)}_{16}$, Remainder = $\text{(5B)}_{16}$.