456332162400 has 1080 divisors, whose sum is σ = 1786129274160. Its totient is φ = 113153863680.

The previous prime is 456332162393. The next prime is 456332162401. The reversal of 456332162400 is 4261233654.

456332162400 is a `hidden beast` number, since 4 + 5 + 6 + 3 + 3 + 21 + 624 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1080).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (456332162401) by changing a digit.

It is a polite number, since it can be written in 179 ways as a sum of consecutive naturals, for example, 4186533546 + ... + 4186533654.

It is an arithmetic number, because the mean of its divisors is an integer number (1653823402).

Almost surely, 2^456332162400 is an apocalyptic number.

456332162400 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 456332162400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (893064637080).

456332162400 is an abundant number, since it is smaller than the sum of its proper divisors (1329797111760).

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

456332162400 is a wasteful number, since it uses less digits than its factorization.

456332162400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 270 (or 195 counting only the distinct ones).

The product of its (nonzero) digits is 103680, while the sum is 36.

The spelling of 456332162400 in words is "four hundred fifty-six billion, three hundred thirty-two million, one hundred sixty-two thousand, four hundred".