72508800 has 384 divisors, whose sum is σ = 297480960. Its totient is φ = 15114240.

The previous prime is 72508753. The next prime is 72508801. The reversal of 72508800 is 880527.

It is a tau number, because it is divible by the number of its divisors (384).

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 (72508801) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 873559 + ... + 873641.

It is an arithmetic number, because the mean of its divisors is an integer number (774690).

Almost surely, 2^72508800 is an apocalyptic number.

72508800 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72508800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (148740480).

72508800 is an abundant number, since it is smaller than the sum of its proper divisors (224972160).

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

72508800 is a wasteful number, since it uses less digits than its factorization.

72508800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 130 (or 113 counting only the distinct ones).

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

The square root of 72508800 is about 8515.2099210765. The cubic root of 72508800 is about 416.9944159032.

The spelling of 72508800 in words is "seventy-two million, five hundred eight thousand, eight hundred".