Question

Find the number of positive divisors of 720.

• A. 24
• B. 30
• C. 36
• D. 40

Hint:

Use prime factorization and $(e_1 + 1)(e_2 + 1)\ldots$ for the number of divisors.

Answer 1

The Correct Option is B

- Step 1: Prime factorization. $720 = 2^4 \cdot 3^2 \cdot 5^1$.
- Step 2: Number of divisors. $(4+1)(2+1)(1+1) = 5 \cdot 3 \cdot 2 = 30$.
- Step 3: Verify. Divisors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 144, 180, 240, 360, 720. Count = 30.
- Step 4: Conclusion. Option (2) 30 is correct.