72640800 has 360 divisors, whose sum is σ = 283575600. Its totient is φ = 18040320.

The previous prime is 72640783. The next prime is 72640801. The reversal of 72640800 is 804627.

It is a tau number, because it is divible by the number of its divisors (360).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (72640801) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 1231171 + ... + 1231229.

It is an arithmetic number, because the mean of its divisors is an integer number (787710).

Almost surely, 2^72640800 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 72640800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (141787800).

72640800 is an abundant number, since it is smaller than the sum of its proper divisors (210934800).

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

72640800 is a wasteful number, since it uses less digits than its factorization.

72640800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 110 (or 88 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

The square root of 72640800 is about 8522.9572332612. The cubic root of 72640800 is about 417.2473042659.

The spelling of 72640800 in words is "seventy-two million, six hundred forty thousand, eight hundred".