456424214400 has 1152 divisors, whose sum is σ = 2150113455360. Its totient is φ = 89255116800.

The previous prime is 456424214291. The next prime is 456424214419. The reversal of 456424214400 is 4412424654.

456424214400 is a `hidden beast` number, since 4 + 5 + 6 + 4 + 242 + 1 + 4 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 37693147 + ... + 37705253.

It is an arithmetic number, because the mean of its divisors is an integer number (1866417930).

Almost surely, 2^456424214400 is an apocalyptic number.

456424214400 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 456424214400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1075056727680).

456424214400 is an abundant number, since it is smaller than the sum of its proper divisors (1693689240960).

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

456424214400 is a wasteful number, since it uses less digits than its factorization.

456424214400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 12172 (or 12152 counting only the distinct ones).

The product of its (nonzero) digits is 122880, while the sum is 36.

The spelling of 456424214400 in words is "four hundred fifty-six billion, four hundred twenty-four million, two hundred fourteen thousand, four hundred".