72186400 has 144 divisors (see below), whose sum is σ = 207361728. Its totient is φ = 24192000.

The previous prime is 72186319. The next prime is 72186409. The reversal of 72186400 is 468127.

It is not an unprimeable number, because it can be changed into a prime (72186409) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 114085 + ... + 114715.

It is an arithmetic number, because the mean of its divisors is an integer number (1440012).

Almost surely, 2^72186400 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 72186400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (103680864).

72186400 is an abundant number, since it is smaller than the sum of its proper divisors (135175328).

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

72186400 is a wasteful number, since it uses less digits than its factorization.

72186400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 675 (or 662 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 28.

The square root of 72186400 is about 8496.2579998491. The cubic root of 72186400 is about 416.3754623052.

The spelling of 72186400 in words is "seventy-two million, one hundred eighty-six thousand, four hundred".