72964800 has 210 divisors, whose sum is σ = 268676628. Its totient is φ = 19422720.

The previous prime is 72964753. The next prime is 72964811. The reversal of 72964800 is 846927.

72964800 is a `hidden beast` number, since 7 + 2 + 9 + 648 + 0 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 129319 + ... + 129881.

Almost surely, 2^72964800 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 72964800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (134338314).

72964800 is an abundant number, since it is smaller than the sum of its proper divisors (195711828).

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

72964800 is a wasteful number, since it uses less digits than its factorization.

72964800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 597 (or 573 counting only the distinct ones).

The product of its (nonzero) digits is 24192, while the sum is 36.

The square root of 72964800 is about 8541.9435727474. The cubic root of 72964800 is about 417.8667340712.

The spelling of 72964800 in words is "seventy-two million, nine hundred sixty-four thousand, eight hundred".