72815511316800 has 1008 divisors, whose sum is σ = 281312156744640. Its totient is φ = 16439804559360.

The previous prime is 72815511316729. The next prime is 72815511316853. The reversal of 72815511316800 is 861311551827.

It is a happy number.

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 72815511316800.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 12844504366 + ... + 12844510034.

It is an arithmetic number, because the mean of its divisors is an integer number (279079520580).

Almost surely, 2^{72815511316800} is an apocalyptic number.

72815511316800 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 72815511316800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (140656078372320).

72815511316800 is an abundant number, since it is smaller than the sum of its proper divisors (208496645427840).

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

72815511316800 is a wasteful number, since it uses less digits than its factorization.

72815511316800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 6368 (or 6346 counting only the distinct ones).

The product of its (nonzero) digits is 403200, while the sum is 48.

The spelling of 72815511316800 in words is "seventy-two trillion, eight hundred fifteen billion, five hundred eleven million, three hundred sixteen thousand, eight hundred".