3840 has 36 divisors (see below), whose sum is σ = 12264. Its totient is φ = 1024.

The previous prime is 3833. The next prime is 3847. The reversal of 3840 is 483.

3840 = T_{11} + T_{12} + ... +
T_{28}.

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 an interprime number because it is at equal distance from previous prime (3833) and next prime (3847).

It is a Harshad number since it is a multiple of its sum of digits (15).

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 Saint-Exupery number, since it is equal to the product of the sides of a Pythagorean triangle: 20 × 12 × 16.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (3847) by changing a digit.

In principle, a polygon with 3840 sides can be constructed with ruler and compass.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 766 + ... + 770.

2^{3840} 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).

3840 is an abundant number, since it is smaller than the sum of its proper divisors (8424).

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 sum of its prime factors is 24 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 15.

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 = 240^{2}).

3840 divided by its sum of digits (15) gives a 8-th power (256 = 2^{8}).

It can be divided in two parts, 38 and 40, that added together give a triangular number (78 = T_{12}).

The spelling of 3840 in words is "three thousand, eight hundred forty".

Divisors: 1 2 3 4 5 6 8 10 12 15 16 20 24 30 32 40 48 60 64 80 96 120 128 160 192 240 256 320 384 480 640 768 960 1280 1920 3840

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