193824 has 36 divisors (see below), whose sum is σ = 552006. Its totient is φ = 64512.

The previous prime is 193813. The next prime is 193841. The reversal of 193824 is 428391.

193824 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in only one way, i.e., 176400 + 17424 = 420^2 + 132^2 .

It is a tau number, because it is divible by the number of its divisors (36).

It is a nude number because it is divisible by every one of its digits.

It is one of the 548 Lynch-Bell numbers.

It is a nialpdrome in base 12.

It is a congruent number.

It is an unprimeable number.

193824 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 49 + ... + 624.

2¹⁹³⁸²⁴ 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 193824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (276003).

193824 is an abundant number, since it is smaller than the sum of its proper divisors (358182).

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

193824 is a wasteful number, since it uses less digits than its factorization.

193824 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 689 (or 678 counting only the distinct ones).

The product of its digits is 1728, while the sum is 27.

The square root of 193824 is about 440.2544718683. The cubic root of 193824 is about 57.8720922895.

The spelling of 193824 in words is "one hundred ninety-three thousand, eight hundred twenty-four".