727632000 has 384 divisors, whose sum is σ = 2713950720. Its totient is φ = 186624000.

The previous prime is 727631987. The next prime is 727632013. The reversal of 727632000 is 236727.

727632000 is a `hidden beast` number, since 7 + 27 + 632 + 0 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (727631987) and next prime (727632013).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 4463919 + ... + 4464081.

It is an arithmetic number, because the mean of its divisors is an integer number (7067580).

Almost surely, 2^727632000 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 727632000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1356975360).

727632000 is an abundant number, since it is smaller than the sum of its proper divisors (1986318720).

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

727632000 is a wasteful number, since it uses less digits than its factorization.

727632000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 229 (or 204 counting only the distinct ones).

The product of its (nonzero) digits is 3528, while the sum is 27.

The square root of 727632000 is about 26974.6547707288. The cubic root of 727632000 is about 899.4366845280.

Adding to 727632000 its reverse (236727), we get a palindrome (727868727).

The spelling of 727632000 in words is "seven hundred twenty-seven million, six hundred thirty-two thousand".