Owlet puzzle #28
Released Sunday, August 2, 2026 UTC
720
the answer for puzzle #28
The five clues
- A three-digit multiple of thirty-six.
- A three-digit factorial.
- The smallest number with exactly 30 divisors.
- Its prime factorization is 2⁴·3²·5, giving τ = 5·3·2 = 30 divisors.
- Also equals 6! — the number of ways to permute six distinct objects.
Backstory
720 = 6! = 8 × 9 × 10 — the number of ways to arrange six distinct objects, and the product of three consecutive integers. Its factorization 2⁴ · 3² · 5 makes it highly composite: 720 has 30 divisors, more than any smaller number.
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