72005919321600 has 1920 divisors, whose sum is σ = 292000070799360. Its totient is φ = 17235099648000.

The previous prime is 72005919321551. The next prime is 72005919321601. The reversal of 72005919321600 is 612391950027.

It is a happy number.

72005919321600 is a `hidden beast` number, since 7 + 2 + 0 + 0 + 5 + 9 + 1 + 9 + 32 + 1 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (1920).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72005919321601) by changing a digit.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 133097817330 + ... + 133097817870.

It is an arithmetic number, because the mean of its divisors is an integer number (152083370208).

Almost surely, 2^{72005919321600} 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 72005919321600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (146000035399680).

72005919321600 is an abundant number, since it is smaller than the sum of its proper divisors (219994151477760).

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

72005919321600 is a wasteful number, since it uses less digits than its factorization.

72005919321600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 969 (or 942 counting only the distinct ones).

The product of its (nonzero) digits is 204120, while the sum is 45.

The spelling of 72005919321600 in words is "seventy-two trillion, five billion, nine hundred nineteen million, three hundred twenty-one thousand, six hundred".