72408189600 has 288 divisors, whose sum is σ = 262201343040. Its totient is φ = 19284894720.

The previous prime is 72408189599. The next prime is 72408189619. The reversal of 72408189600 is 698180427.

72408189600 is a `hidden beast` number, since 7 + 2 + 408 + 189 + 60 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-2 number, since 2×72408189600² (a number of 23 digits) contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 23607267 + ... + 23610333.

It is an arithmetic number, because the mean of its divisors is an integer number (910421330).

Almost surely, 2^72408189600 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 72408189600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131100671520).

72408189600 is an abundant number, since it is smaller than the sum of its proper divisors (189793153440).

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

72408189600 is a wasteful number, since it uses less digits than its factorization.

72408189600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 4189 (or 4170 counting only the distinct ones).

The product of its (nonzero) digits is 193536, while the sum is 45.

The spelling of 72408189600 in words is "seventy-two billion, four hundred eight million, one hundred eighty-nine thousand, six hundred".