72586400 has 72 divisors (see below), whose sum is σ = 181605564. Its totient is φ = 28313600.

The previous prime is 72586373. The next prime is 72586417. The reversal of 72586400 is 468527.

It can be written as a sum of positive squares in 6 ways, for example, as 30958096 + 41628304 = 5564^2 + 6452^2 .

It is a Harshad number since it is a multiple of its sum of digits (32).

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 31694 + ... + 33906.

Almost surely, 2^72586400 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 72586400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (90802782).

72586400 is an abundant number, since it is smaller than the sum of its proper divisors (109019164).

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

72586400 is a wasteful number, since it uses less digits than its factorization.

72586400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2274 (or 2261 counting only the distinct ones).

The product of its (nonzero) digits is 13440, while the sum is 32.

The square root of 72586400 is about 8519.7652549821. The cubic root of 72586400 is about 417.1431207497.

The spelling of 72586400 in words is "seventy-two million, five hundred eighty-six thousand, four hundred".