72192000 has 208 divisors, whose sum is σ = 245336832. Its totient is φ = 18841600.

The previous prime is 72191993. The next prime is 72192011. The reversal of 72192000 is 29127.

It is a happy number.

It is a hoax number, since the sum of its digits (21) coincides with the sum of the digits of its distinct prime factors.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1535977 + ... + 1536023.

It is an arithmetic number, because the mean of its divisors is an integer number (1179504).

Almost surely, 2^72192000 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 72192000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (122668416).

72192000 is an abundant number, since it is smaller than the sum of its proper divisors (173144832).

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

72192000 is an equidigital number, since it uses as much as digits as its factorization.

72192000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 89 (or 57 counting only the distinct ones).

The product of its (nonzero) digits is 252, while the sum is 21.

The square root of 72192000 is about 8496.5875503051. The cubic root of 72192000 is about 416.3862290715.

It can be divided in two parts, 72 and 192000, that multiplied together give a cube (13824000 = 240³).

The spelling of 72192000 in words is "seventy-two million, one hundred ninety-two thousand".