72588000 has 192 divisors, whose sum is σ = 249080832. Its totient is φ = 18444800.

The previous prime is 72587989. The next prime is 72588007. The reversal of 72588000 is 88527.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72588007) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 275869 + ... + 276131.

It is an arithmetic number, because the mean of its divisors is an integer number (1297296).

Almost surely, 2^72588000 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 72588000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (124540416).

72588000 is an abundant number, since it is smaller than the sum of its proper divisors (176492832).

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

72588000 is a wasteful number, since it uses less digits than its factorization.

72588000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 314 (or 296 counting only the distinct ones).

The product of its (nonzero) digits is 4480, while the sum is 30.

The square root of 72588000 is about 8519.8591537654. The cubic root of 72588000 is about 417.1461857136.

The spelling of 72588000 in words is "seventy-two million, five hundred eighty-eight thousand".