72985568947200 has 6336 divisors, whose sum is σ = 368804854978560. Its totient is φ = 13341535764480.

The previous prime is 72985568947141. The next prime is 72985568947201. The reversal of 72985568947200 is 274986558927.

72985568947200 is a `hidden beast` number, since 7 + 2 + 9 + 8 + 556 + 8 + 9 + 47 + 20 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is not an unprimeable number, because it can be changed into a prime (72985568947201) by changing a digit.

It is a polite number, since it can be written in 575 ways as a sum of consecutive naturals, for example, 237738009447 + ... + 237738009753.

It is an arithmetic number, because the mean of its divisors is an integer number (58207836960).

Almost surely, 2^{72985568947200} is an apocalyptic number.

72985568947200 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 72985568947200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (184402427489280).

72985568947200 is an abundant number, since it is smaller than the sum of its proper divisors (295819286031360).

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

72985568947200 is a wasteful number, since it uses less digits than its factorization.

72985568947200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 432 (or 406 counting only the distinct ones).

The product of its (nonzero) digits is 609638400, while the sum is 72.

The spelling of 72985568947200 in words is "seventy-two trillion, nine hundred eighty-five billion, five hundred sixty-eight million, nine hundred forty-seven thousand, two hundred".