406400 has 48 divisors (see below), whose sum is σ = 1011840. Its totient is φ = 161280.

The previous prime is 406397. The next prime is 406403. The reversal of 406400 is 4604.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (406397) and next prime (406403).

It is a zygodrome in base 2.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (406403) by changing a digit.

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 5 ways as a sum of consecutive naturals, for example, 3137 + ... + 3263.

It is an arithmetic number, because the mean of its divisors is an integer number (21080).

2⁴⁰⁶⁴⁰⁰ is an apocalyptic number.

406400 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 406400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (505920).

406400 is an abundant number, since it is smaller than the sum of its proper divisors (605440).

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

406400 is a wasteful number, since it uses less digits than its factorization.

406400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 151 (or 134 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 14.

The square root of 406400 is about 637.4950980204. The cubic root of 406400 is about 74.0715159610.

The spelling of 406400 in words is "four hundred six thousand, four hundred".