72165038400 has 1680 divisors, whose sum is σ = 339332864640. Its totient is φ = 14631321600.

The previous prime is 72165038399. The next prime is 72165038419. The reversal of 72165038400 is 483056127.

72165038400 is a `hidden beast` number, since 7 + 216 + 5 + 0 + 38 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (1680).

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 a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 342014295 + ... + 342014505.

It is an arithmetic number, because the mean of its divisors is an integer number (201983848).

Almost surely, 2^72165038400 is an apocalyptic number.

72165038400 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 72165038400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (169666432320).

72165038400 is an abundant number, since it is smaller than the sum of its proper divisors (267167826240).

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

72165038400 is a wasteful number, since it uses less digits than its factorization.

72165038400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 294 (or 270 counting only the distinct ones).

The product of its (nonzero) digits is 40320, while the sum is 36.

The spelling of 72165038400 in words is "seventy-two billion, one hundred sixty-five million, thirty-eight thousand, four hundred".