98304 has 32 divisors (see below), whose sum is σ = 262140. Its totient is φ = 32768.

The previous prime is 98299. The next prime is 98317. The reversal of 98304 is 40389.

It is a Jordan-Polya number, since it can be written as 4! ⋅ (2!)¹².

It is a tau number, because it is divible by the number of its divisors (32).

It is an ABA number since it can be written as A⋅B^A, here for A=3, B=32.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a nialpdrome in base 2 and base 8.

It is a zygodrome in base 2.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

In principle, a polygon with 98304 sides can be constructed with ruler and compass.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 32767 + 32768 + 32769.

98304 is a Friedman number, since it can be written as 8^(9-4-0)*3, using all its digits and the basic arithmetic operations.

2⁹⁸³⁰⁴ 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 98304, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131070).

98304 is an abundant number, since it is smaller than the sum of its proper divisors (163836).

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

98304 is an frugal number, since it uses more digits than its factorization.

98304 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 33 (or 5 counting only the distinct ones).

The product of its (nonzero) digits is 864, while the sum is 24.

The square root of 98304 is about 313.5346870762. The cubic root of 98304 is about 46.1519862498.

Multiplying 98304 by its sum of digits (24), we get a square (2359296 = 1536²).

98304 divided by its sum of digits (24) gives a 12-th power (4096 = 2¹²).

Multiplying 98304 by its product of nonzero digits (864), we get a 4-th power (84934656 = 96⁴).

It can be divided in two parts, 98 and 304, that multiplied together give a palindrome (29792).

The spelling of 98304 in words is "ninety-eight thousand, three hundred four".