72460800 has 360 divisors, whose sum is σ = 281991996. Its totient is φ = 17694720.

The previous prime is 72460789. The next prime is 72460831. The reversal of 72460800 is 806427.

It can be written as a sum of positive squares in 6 ways, for example, as 52533504 + 19927296 = 7248^2 + 4464^2 .

It is a tau number, because it is divible by the number of its divisors (360).

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, 1958382 + ... + 1958418.

Almost surely, 2^72460800 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 72460800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (140995998).

72460800 is an abundant number, since it is smaller than the sum of its proper divisors (209531196).

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

72460800 is a wasteful number, since it uses less digits than its factorization.

72460800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 88 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

The square root of 72460800 is about 8512.3909684647. The cubic root of 72460800 is about 416.9023804063.

It can be divided in two parts, 72 and 460800, that multiplied together give a square (33177600 = 5760²).

The spelling of 72460800 in words is "seventy-two million, four hundred sixty thousand, eight hundred".