406368 has 72 divisors (see below), whose sum is σ = 1238328. Its totient is φ = 125952.

The previous prime is 406361. The next prime is 406381. The reversal of 406368 is 863604.

It is a tau number, because it is divible by the number of its divisors (72).

It is an Ulam number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (406361) by changing a digit.

406368 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 4855 + ... + 4937.

It is an arithmetic number, because the mean of its divisors is an integer number (17199).

2⁴⁰⁶³⁶⁸ is an apocalyptic number.

406368 is a gapful number since it is divisible by the number (48) 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 406368, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (619164).

406368 is an abundant number, since it is smaller than the sum of its proper divisors (831960).

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

406368 is a wasteful number, since it uses less digits than its factorization.

406368 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 116 (or 105 counting only the distinct ones).

The product of its (nonzero) digits is 3456, while the sum is 27.

The square root of 406368 is about 637.4699992941. The cubic root of 406368 is about 74.0695717757.

The spelling of 406368 in words is "four hundred six thousand, three hundred sixty-eight".