72509836800 has 960 divisors, whose sum is σ = 274000320000. Its totient is φ = 16804085760.

The previous prime is 72509836793. The next prime is 72509836807. The reversal of 72509836800 is 863890527.

It is an interprime number because it is at equal distance from previous prime (72509836793) and next prime (72509836807).

It is a tau number, because it is divible by the number of its divisors (960).

It is a Harshad number since it is a multiple of its sum of digits (48).

It is a self number, because there is not a number n which added to its sum of digits gives 72509836800.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72509836807) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 486643126 + ... + 486643274.

It is an arithmetic number, because the mean of its divisors is an integer number (285417000).

Almost surely, 2^72509836800 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 72509836800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (137000160000).

72509836800 is an abundant number, since it is smaller than the sum of its proper divisors (201490483200).

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

72509836800 is a wasteful number, since it uses less digits than its factorization.

72509836800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 251 (or 230 counting only the distinct ones).

The product of its (nonzero) digits is 725760, while the sum is 48.

The spelling of 72509836800 in words is "seventy-two billion, five hundred nine million, eight hundred thirty-six thousand, eight hundred".