To convert 562,741 from base 10 (decimal) to base 8 (octal), we repeatedly divide by 8 and record the remainders. Let's do that:

1. $562,741 \div 8 = 70,342$ remainder $5$
2. $70,342 \div 8 = 8,792$ remainder $6$
3. $8,792 \div 8 = 1,099$ remainder $0$
4. $1,099 \div 8 = 137$ remainder $3$
5. $137 \div 8 = 17$ remainder $1$
6. $17 \div 8 = 2$ remainder $1$
7. $2 \div 8 = 0$ remainder $2$

Now, reading the remainders from bottom to top, we get: 2 1 1 3 0 6 5

Thus, $562,741_{10}$ is equal to 2113065 in base 8.

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:

1. How would you convert 1,234,567 from base 10 to base 8?
2. What is the base 8 representation of 256?
3. How can you convert a number from base 8 back to base 10?
4. How does the process of converting to base 8 differ from converting to base 2?
5. What are the advantages of using base 8 in computer systems?

Tip: When converting between number bases, always read the remainders from bottom to top for the final result.