456400 has 60 divisors (see below), whose sum is σ = 1260832. Its totient is φ = 155520.

The previous prime is 456377. The next prime is 456403. The reversal of 456400 is 4654.

456400 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (456403) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2719 + ... + 2881.

2⁴⁵⁶⁴⁰⁰ is an apocalyptic number.

456400 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 456400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (630416).

456400 is an abundant number, since it is smaller than the sum of its proper divisors (804432).

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

456400 is a wasteful number, since it uses less digits than its factorization.

456400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 188 (or 177 counting only the distinct ones).

The product of its (nonzero) digits is 480, while the sum is 19.

The square root of 456400 is about 675.5738301622. The cubic root of 456400 is about 76.9925219027.

The spelling of 456400 in words is "four hundred fifty-six thousand, four hundred".