456710400 has 270 divisors, whose sum is σ = 1690583202. Its totient is φ = 121651200.

The previous prime is 456710399. The next prime is 456710417. The reversal of 456710400 is 4017654.

It can be written as a sum of positive squares in 3 ways, for example, as 2509056 + 454201344 = 1584^2 + 21312^2 .

It is a tau number, because it is divible by the number of its divisors (270).

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 517960 + ... + 518840.

Almost surely, 2^456710400 is an apocalyptic number.

456710400 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 456710400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (845291601).

456710400 is an abundant number, since it is smaller than the sum of its proper divisors (1233872802).

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

456710400 is an equidigital number, since it uses as much as digits as its factorization.

456710400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 919 (or 891 counting only the distinct ones).

The product of its (nonzero) digits is 3360, while the sum is 27.

The square root of 456710400 is about 21370.7837947044. The cubic root of 456710400 is about 770.0997228464.

The spelling of 456710400 in words is "four hundred fifty-six million, seven hundred ten thousand, four hundred".