It is a Jordan-Polya number, since it can be written as 5! ⋅ (2!)5.
It is a double factorial (3840 = 10 !! = 2 ⋅ 4 ⋅ 6 ⋅ 8 ⋅ 10 ).
3840 is an esthetic number in base 15, because in such base its adjacent digits differ by 1.
It is a nialpdrome in base 2, base 4, base 8 and base 16.
It is a zygodrome in base 2 and base 4.
It is a congruent number.
In principle, a polygon with 3840 sides can be constructed with ruler and compass.
23840 is an apocalyptic number.
3840 is a gapful number since it is divisible by the number (30) formed by its first and last digit.
It is an amenable number.
It is a practical number, because each smaller number is the sum of distinct divisors of 3840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (6132).
It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.
3840 is an equidigital number, since it uses as much as digits as its factorization.
3840 is an evil number, because the sum of its binary digits is even.
The square root of 3840 is about 61.9677335393. The cubic root of 3840 is about 15.6594705647.
Multiplying 3840 by its sum of digits (15), we get a square (57600 = 2402).
3840 divided by its sum of digits (15) gives a 8-th power (256 = 28).
The spelling of 3840 in words is "three thousand, eight hundred forty".