72812390400 has 720 divisors, whose sum is σ = 273967113420. Its totient is φ = 19110297600.

The previous prime is 72812390377. The next prime is 72812390423. The reversal of 72812390400 is 409321827.

72812390400 is a `hidden beast` number, since 72 + 81 + 23 + 90 + 400 = 666.

It is an interprime number because it is at equal distance from previous prime (72812390377) and next prime (72812390423).

It can be written as a sum of positive squares in 6 ways, for example, as 5478368256 + 67334022144 = 74016^2 + 259488^2 .

It is a tau number, because it is divible by the number of its divisors (720).

It is a hoax number, since the sum of its digits (36) 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 (36).

It is an unprimeable number.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 402278310 + ... + 402278490.

Almost surely, 2^72812390400 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72812390400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (136983556710).

72812390400 is an abundant number, since it is smaller than the sum of its proper divisors (201154723020).

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

72812390400 is a wasteful number, since it uses less digits than its factorization.

72812390400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 322 (or 288 counting only the distinct ones).

The product of its (nonzero) digits is 24192, while the sum is 36.

The spelling of 72812390400 in words is "seventy-two billion, eight hundred twelve million, three hundred ninety thousand, four hundred".