91728000 has 576 divisors, whose sum is σ = 412677720. Its totient is φ = 19353600.

The previous prime is 91727983. The next prime is 91728037. The reversal of 91728000 is 82719.

It can be written as a sum of positive squares in 4 ways, for example, as 12446784 + 79281216 = 3528^2 + 8904^2 .

It is a tau number, because it is divible by the number of its divisors (576).

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 7055994 + ... + 7056006.

Almost surely, 2^91728000 is an apocalyptic number.

91728000 is a gapful number since it is divisible by the number (90) 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 91728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (206338860).

91728000 is an abundant number, since it is smaller than the sum of its proper divisors (320949720).

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

91728000 is a wasteful number, since it uses less digits than its factorization.

91728000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 62 (or 30 counting only the distinct ones).

The product of its (nonzero) digits is 1008, while the sum is 27.

The square root of 91728000 is about 9577.4735708328. The cubic root of 91728000 is about 450.9904111838.

The spelling of 91728000 in words is "ninety-one million, seven hundred twenty-eight thousand".