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The problem is asking to convert the base-10 number \(1642\) into a base-7 number. Let's walk through the process of conversion.

### Steps to Convert from Base-10 to Base-7:

1. **Divide the number by 7** and record the quotient and remainder.
2. **Repeat** the division process on the quotient until the quotient is 0.
3. The base-7 number will be the sequence of remainders read **from bottom to top**.

### Calculation:

1. \( 1642 \div 7 = 234 \) remainder \(4\)
2. \( 234 \div 7 = 33 \) remainder \(3\)
3. \( 33 \div 7 = 4 \) remainder \(5\)
4. \( 4 \div 7 = 0 \) remainder \(4\)

Now, reading the remainders from bottom to top, we get the base-7 number:

**Result: \( 4534_7 \)**

So, \( 1642_{10} = 4534_7 \).

Would you like a further breakdown of the steps? Let me know if you need details or have any questions!

Here are five related questions:
1. How would you convert a base-7 number back to base-10?
2. What is the base-7 equivalent of \(2000\)?
3. How do you convert a base-10 fraction to base-7?
4. What is the difference between base-7 and base-8 number systems?
5. How can you check if a conversion to base-7 is correct?

**Tip:** Always verify your result by converting the base-7 number back to base-10 for accuracy!

Convert from 1642, a BASE-10 NUMBER to a BASE-7 NUMBER.

Learn how to convert the base-10 number 1642 to its base-7 equivalent using step-by-step division. This problem focuses on number systems and base conversions, suitable for students in Grades 6-9.

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