Number Gossip

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Unique Properties of 720

  • 720 is the largest factorial to contain all different digits
  • 720 is the smallest number with 30 divisors
  • 720 is the smallest number n such that τ(n)φ(n) > prime(n)
  • 720 is the smallest number n such that σ(n)2 is greater than 3σ(n2)
  • 720 is the smallest number n such that prime(n) ± n and prime(n) ± 2n are all primes
  • 720 is the smallest number n where either n or n+1 is divisible by the numbers from 1 to 10
  • 720 is the product of the sides and the perimeter of the smallest Pythagorean triangle
  • 720 is the smallest positive number differing from the next 3 greater squares by squares (720 = 272 - 32 = 282 - 82 = 292 - 112)

Rare Properties of 720

Factorial

Common Properties of 720

Abundant
Apocalyptic power
Composite
Even
Evil
Practical
Ulam