193872 has 40 divisors (see below), whose sum is σ = 573376. Its totient is φ = 55296.

The previous prime is 193871. The next prime is 193873. The reversal of 193872 is 278391.

It is a happy number.

193872 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (193871) and next prime (193873).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (193871) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 48 + ... + 624.

2¹⁹³⁸⁷² is an apocalyptic number.

193872 is a gapful number since it is divisible by the number (12) 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 193872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (286688).

193872 is an abundant number, since it is smaller than the sum of its proper divisors (379504).

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

193872 is a wasteful number, since it uses less digits than its factorization.

193872 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 595 (or 589 counting only the distinct ones).

The product of its digits is 3024, while the sum is 30.

The square root of 193872 is about 440.3089824203. The cubic root of 193872 is about 57.8768691853.

The spelling of 193872 in words is "one hundred ninety-three thousand, eight hundred seventy-two".