37728000 has 216 divisors, whose sum is σ = 136792656. Its totient is φ = 9984000.

The previous prime is 37727983. The next prime is 37728001. The reversal of 37728000 is 82773.

37728000 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (37728001) by changing a digit.

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 23 ways as a sum of consecutive naturals, for example, 287935 + ... + 288065.

Almost surely, 2^37728000 is an apocalyptic number.

37728000 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 37728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (68396328).

37728000 is an abundant number, since it is smaller than the sum of its proper divisors (99064656).

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

37728000 is a wasteful number, since it uses less digits than its factorization.

37728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 168 (or 141 counting only the distinct ones).

The product of its (nonzero) digits is 2352, while the sum is 27.

The square root of 37728000 is about 6142.3122681935. The cubic root of 37728000 is about 335.3934635819.

The spelling of 37728000 in words is "thirty-seven million, seven hundred twenty-eight thousand".