1. The problem is to divide the octal number 665 by 6. 2. First, convert the octal number 665 to decimal. Octal digits represent powers of 8, so: $$665_8 = 6 \times 8^2 + 6 \times 8^1 + 5 \times 8^0$$ 3. Calculate each term: $$6 \times 64 = 384$$ $$6 \times 8 = 48$$ $$5 \times 1 = 5$$ 4. Sum these values to get the decimal equivalent: $$384 + 48 + 5 = 437$$ 5. Now divide the decimal number 437 by 6: $$437 \div 6 = 72.8333...$$ 6. To express the result back in octal, convert the integer part 72 to octal: Divide 72 by 8: $$72 \div 8 = 9 \text{ remainder } 0$$ Divide 9 by 8: $$9 \div 8 = 1 \text{ remainder } 1$$ Divide 1 by 8: $$1 \div 8 = 0 \text{ remainder } 1$$ Reading remainders from last to first gives: $$110_8$$ 7. The decimal remainder is: $$437 - 72 \times 6 = 437 - 432 = 5$$ 8. To express the fractional part in octal, multiply the decimal remainder by 8 and divide by 6 repeatedly or convert the decimal fraction 0.8333... to octal fraction approximately. 9. For simplicity, the approximate octal result is: $$110.6_8$$ (since 0.8333 \times 8 \approx 6.666) Final answer: The division of octal 665 by 6 is approximately $$110.6_8$$ in octal or 72.8333 in decimal.