72719817984000 has 3072 divisors, whose sum is σ = 313678813593600. Its totient is φ = 16424239104000.

The previous prime is 72719817983977. The next prime is 72719817984013. The reversal of 72719817984000 is 48971891727.

72719817984000 is a `hidden beast` number, since 7 + 2 + 71 + 98 + 1 + 79 + 8 + 400 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (3072).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 255 ways as a sum of consecutive naturals, for example, 164153087779 + ... + 164153088221.

It is an arithmetic number, because the mean of its divisors is an integer number (102108988800).

Almost surely, 2^{72719817984000} 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 72719817984000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (156839406796800).

72719817984000 is an abundant number, since it is smaller than the sum of its proper divisors (240958995609600).

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

72719817984000 is a wasteful number, since it uses less digits than its factorization.

72719817984000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 644 (or 608 counting only the distinct ones).

The product of its (nonzero) digits is 14224896, while the sum is 63.

The spelling of 72719817984000 in words is "seventy-two trillion, seven hundred nineteen billion, eight hundred seventeen million, nine hundred eighty-four thousand".