72385034400 has 1512 divisors, whose sum is σ = 328519403100. Its totient is φ = 15467397120.

The previous prime is 72385034357. The next prime is 72385034411. The reversal of 72385034400 is 443058327.

It is a happy number.

It can be written as a sum of positive squares in 6 ways, for example, as 21289144464 + 51095889936 = 145908^2 + 226044^2 .

It is a tau number, because it is divible by the number of its divisors (1512).

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 pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 251 ways as a sum of consecutive naturals, for example, 485805526 + ... + 485805674.

Almost surely, 2^72385034400 is an apocalyptic number.

72385034400 is a gapful number since it is divisible by the number (70) 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 72385034400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (164259701550).

72385034400 is an abundant number, since it is smaller than the sum of its proper divisors (256134368700).

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

72385034400 is a wasteful number, since it uses less digits than its factorization.

72385034400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 218 (or 183 counting only the distinct ones).

The product of its (nonzero) digits is 80640, while the sum is 36.

The spelling of 72385034400 in words is "seventy-two billion, three hundred eighty-five million, thirty-four thousand, four hundred".