Highly Divisible
Friends everywhere — 24 divisors minimum.
A number with 24 or more divisors, like 360 (exactly 24) or 720720 (240). The social butterflies of the composite world.
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The range holds 189,218 highly divisible numbers, about 18.9% — not rare, but it rewards numbers with thick prime factorizations: only by stacking high exponents on small primes like 2, 3 and 5 can the divisor count (the product of each exponent plus one) climb to 24.
The gatekeeper is 360, with exactly 24 divisors — which is probably why Mesopotamians loved it: about 360 days a year, 360 degrees a circle, divisible every which way. The divisor king of the range is 720720 with 240 divisors, tied by 831600 and 997920.
Trivia: from 6! = 720 onward, every factorial in range is highly divisible — factorials inherit every prime factor along the way, so they can hardly help being sociable. If you're hunting this feature, multiples of 60 are a shortcut.