72829238400 has 576 divisors, whose sum is σ = 273400938720. Its totient is φ = 19140157440.

The previous prime is 72829238303. The next prime is 72829238407. The reversal of 72829238400 is 483292827.

72829238400 is a `hidden beast` number, since 7 + 2 + 8 + 2 + 9 + 238 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (576).

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

It is not an unprimeable number, because it can be changed into a prime (72829238407) by changing a digit.

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 71 ways as a sum of consecutive naturals, for example, 56764159 + ... + 56765441.

Almost surely, 2^72829238400 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 72829238400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (136700469360).

72829238400 is an abundant number, since it is smaller than the sum of its proper divisors (200571700320).

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

72829238400 is a wasteful number, since it uses less digits than its factorization.

72829238400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1395 (or 1366 counting only the distinct ones).

The product of its (nonzero) digits is 387072, while the sum is 45.

The spelling of 72829238400 in words is "seventy-two billion, eight hundred twenty-nine million, two hundred thirty-eight thousand, four hundred".