1. **State the problem:** Multiply the octal numbers 527 (base 8) and 673 (base 8). 2. **Convert octal to decimal:** - $527_8 = 5 \times 8^2 + 2 \times 8^1 + 7 \times 8^0 = 5 \times 64 + 2 \times 8 + 7 = 320 + 16 + 7 = 343_{10}$ - $673_8 = 6 \times 8^2 + 7 \times 8^1 + 3 \times 8^0 = 6 \times 64 + 7 \times 8 + 3 = 384 + 56 + 3 = 443_{10}$ 3. **Multiply the decimal equivalents:** $$343 \times 443 = 151,849$$ 4. **Convert the product back to octal:** Divide 151,849 by 8 repeatedly and record remainders: - $151,849 \div 8 = 18,981$ remainder $1$ - $18,981 \div 8 = 2,372$ remainder $5$ - $2,372 \div 8 = 296$ remainder $4$ - $296 \div 8 = 37$ remainder $0$ - $37 \div 8 = 4$ remainder $5$ - $4 \div 8 = 0$ remainder $4$ Reading remainders from last to first: $450451_8$ 5. **Final answer:** $$527_8 \times 673_8 = 450451_8$$