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Difficulty: 3/102024 NMTC 2024 (QI-13)

What is the sum of all the divisors of 600?

Options:

  • A.

    2060

  • 1860

  • C.

    2160

  • D.

    1890

Guide / Hint

Hint 1: Find the prime factorization of 600.

Hint 2: Recall the sum of divisors formula: .

Hint 3: Calculate to find the sum.

Solution

Step 1 (Prime Factorization): We find the prime factorization of 600:

Step 2 (Sum of Divisors Formula): The sum of all positive divisors of is given by:

For 600, this is:

Step 3 (Conclusion): The sum of all positive divisors of 600 is exactly .

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    2024 NMTC 2024 QI-13 - Olympiad Math Olympiad Question | Leminno