72590400 has 189 divisors, whose sum is σ = 261688453. Its totient is φ = 19084800.

The previous prime is 72590347. The next prime is 72590429. The reversal of 72590400 is 409527.

The square root of 72590400 is 8520.

It is a perfect power (a square), and thus also a powerful number.

72590400 is a `hidden beast` number, since 7 + 259 + 0 + 400 = 666.

It can be written as a sum of positive squares in only one way, i.e., 26132544 + 46457856 = 5112^2 + 6816^2 .

It is a Duffinian number.

It is an unprimeable number.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 1022365 + ... + 1022435.

Almost surely, 2^72590400 is an apocalyptic number.

72590400 is the 8520-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72590400

72590400 is an abundant number, since it is smaller than the sum of its proper divisors (189098053).

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

72590400 is a wasteful number, since it uses less digits than its factorization.

72590400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 170 (or 81 counting only the distinct ones).

The product of its (nonzero) digits is 2520, while the sum is 27.

The cubic root of 72590400 is about 417.1507830751.

Adding to 72590400 its reverse (409527), we get a palindrome (72999927).

It can be divided in two parts, 725 and 90400, that added together give a cube (91125 = 45³).

The spelling of 72590400 in words is "seventy-two million, five hundred ninety thousand, four hundred".