456407078400 has 2160 divisors, whose sum is σ = 2151094312224. Its totient is φ = 90172293120.

The previous prime is 456407078359. The next prime is 456407078443. The reversal of 456407078400 is 4870704654.

456407078400 is a `hidden beast` number, since 4 + 564 + 0 + 7 + 0 + 7 + 84 + 0 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 215 ways as a sum of consecutive naturals, for example, 2316787102 + ... + 2316787298.

Almost surely, 2^456407078400 is an apocalyptic number.

456407078400 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 456407078400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1075547156112).

456407078400 is an abundant number, since it is smaller than the sum of its proper divisors (1694687233824).

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

456407078400 is a wasteful number, since it uses less digits than its factorization.

456407078400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 281 (or 244 counting only the distinct ones).

The product of its (nonzero) digits is 752640, while the sum is 45.

The spelling of 456407078400 in words is "four hundred fifty-six billion, four hundred seven million, seventy-eight thousand, four hundred".