72590800 has 60 divisors (see below), whose sum is σ = 175574700. Its totient is φ = 28840960.

The previous prime is 72590797. The next prime is 72590801. The reversal of 72590800 is 809527.

It can be written as a sum of positive squares in 6 ways, for example, as 7884864 + 64705936 = 2808^2 + 8044^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72590801) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 68676 + ... + 69724.

It is an arithmetic number, because the mean of its divisors is an integer number (2926245).

Almost surely, 2^72590800 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 72590800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (87787350).

72590800 is an abundant number, since it is smaller than the sum of its proper divisors (102983900).

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

72590800 is a wasteful number, since it uses less digits than its factorization.

72590800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1240 (or 1229 counting only the distinct ones).

The product of its (nonzero) digits is 5040, while the sum is 31.

The square root of 72590800 is about 8520.0234741461. The cubic root of 72590800 is about 417.1515492921.

The spelling of 72590800 in words is "seventy-two million, five hundred ninety thousand, eight hundred".