91728 has 90 divisors (see below), whose sum is σ = 321594. Its totient is φ = 24192.

The previous prime is 91711. The next prime is 91733. The reversal of 91728 is 82719.

It can be written as a sum of positive squares in only one way, i.e., 63504 + 28224 = 252^2 + 168^2 .

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is one of the 548 Lynch-Bell numbers.

It is a zygodrome in base 3.

It is a congruent number.

It is an unprimeable number.

91728 is an untouchable number, because it is not equal to the sum of proper divisors of any 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 17 ways as a sum of consecutive naturals, for example, 7050 + ... + 7062.

2⁹¹⁷²⁸ is an apocalyptic number.

91728 is a gapful number since it is divisible by the number (98) 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 91728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (160797).

91728 is an abundant number, since it is smaller than the sum of its proper divisors (229866).

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

91728 is a wasteful number, since it uses less digits than its factorization.

91728 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 41 (or 25 counting only the distinct ones).

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

The square root of 91728 is about 302.8663071390. The cubic root of 91728 is about 45.0990411184.

91728 divided by its product of digits (1008) gives a triangular number (91 = T₁₃).

Subtracting from 91728 its reverse (82719), we obtain a palindrome (9009).

It can be divided in two parts, 9172 and 8, that added together give a triangular number (9180 = T₁₃₅).

The spelling of 91728 in words is "ninety-one thousand, seven hundred twenty-eight".