72314400 has 144 divisors (see below), whose sum is σ = 243734400. Its totient is φ = 18600960.

The previous prime is 72314393. The next prime is 72314441. The reversal of 72314400 is 441327.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 69081 + ... + 70119.

It is an arithmetic number, because the mean of its divisors is an integer number (1692600).

Almost surely, 2^72314400 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 72314400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (121867200).

72314400 is an abundant number, since it is smaller than the sum of its proper divisors (171420000).

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

72314400 is a wasteful number, since it uses less digits than its factorization.

72314400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1091 (or 1078 counting only the distinct ones).

The product of its (nonzero) digits is 672, while the sum is 21.

The square root of 72314400 is about 8503.7873915097. The cubic root of 72314400 is about 416.6214208647.

Adding to 72314400 its reverse (441327), we get a palindrome (72755727).

The spelling of 72314400 in words is "seventy-two million, three hundred fourteen thousand, four hundred".