405768 has 64 divisors (see below), whose sum is σ = 1166400. Its totient is φ = 116480.

The previous prime is 405767. The next prime is 405781. The reversal of 405768 is 867504.

It is a happy number.

It is a Cunningham number, because it is equal to 637²-1.

It is a Smith number, since the sum of its digits (30) coincides with the sum of the digits of its prime factors.

It is a plaindrome in base 13.

It is not an unprimeable number, because it can be changed into a prime (405763) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 7630 + ... + 7682.

It is an arithmetic number, because the mean of its divisors is an integer number (18225).

2⁴⁰⁵⁷⁶⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 405768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (583200).

405768 is an abundant number, since it is smaller than the sum of its proper divisors (760632).

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

405768 is a wasteful number, since it uses less digits than its factorization.

405768 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 102 (or 98 counting only the distinct ones).

The product of its (nonzero) digits is 6720, while the sum is 30.

The square root of 405768 is about 636.9992150702. Note that the first 3 decimals coincide. The cubic root of 405768 is about 74.0330993881.

The spelling of 405768 in words is "four hundred five thousand, seven hundred sixty-eight".