405840 has 80 divisors (see below), whose sum is σ = 1339200. Its totient is φ = 101376.

The previous prime is 405829. The next prime is 405857. The reversal of 405840 is 48504.

405840 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (80).

It is a super-2 number, since 2×405840² = 329412211200, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

405840 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 4516 + ... + 4604.

It is an arithmetic number, because the mean of its divisors is an integer number (16740).

2⁴⁰⁵⁸⁴⁰ is an apocalyptic number.

405840 is a gapful number since it is divisible by the number (40) 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 405840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (669600).

405840 is an abundant number, since it is smaller than the sum of its proper divisors (933360).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

405840 is a wasteful number, since it uses less digits than its factorization.

405840 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 124 (or 118 counting only the distinct ones).

The product of its (nonzero) digits is 640, while the sum is 21.

The square root of 405840 is about 637.0557275467. The cubic root of 405840 is about 74.0374779722.

The spelling of 405840 in words is "four hundred five thousand, eight hundred forty".