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.

Learn how to convert the decimal number 562,741 into its base 8 (octal) equivalent. This detailed step-by-step solution explains the process of dividing by 8 and reading the remainders to get the final result: 2113065 in base 8. Ideal for high school students (Grades 9-12) looking to strengthen their understanding of base conversions.

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