72259200 has 288 divisors, whose sum is σ = 279109740. Its totient is φ = 17694720.

The previous prime is 72259183. The next prime is 72259211. The reversal of 72259200 is 295227.

It is a happy number.

72259200 is a `hidden beast` number, since 72 + 2 + 592 + 0 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 6843456 + 65415744 = 2616^2 + 8088^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 374304 + ... + 374496.

Almost surely, 2^72259200 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 72259200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (139554870).

72259200 is an abundant number, since it is smaller than the sum of its proper divisors (206850540).

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

72259200 is a wasteful number, since it uses less digits than its factorization.

72259200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 236 (or 216 counting only the distinct ones).

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

The square root of 72259200 is about 8500.5411592439. The cubic root of 72259200 is about 416.5153868590.

It can be divided in two parts, 72 and 259200, that multiplied together give a square (18662400 = 4320²).

The spelling of 72259200 in words is "seventy-two million, two hundred fifty-nine thousand, two hundred".