193920 has 64 divisors (see below), whose sum is σ = 624240. Its totient is φ = 51200.

The previous prime is 193891. The next prime is 193937. The reversal of 193920 is 29391.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (64).

It is a Smith number, since the sum of its digits (24) coincides with the sum of the digits of its prime factors.

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

It is an Ulam number.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1870 + ... + 1970.

2¹⁹³⁹²⁰ is an apocalyptic number.

193920 is a gapful number since it is divisible by the number (10) 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 193920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (312120).

193920 is an abundant number, since it is smaller than the sum of its proper divisors (430320).

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

193920 is a wasteful number, since it uses less digits than its factorization.

193920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 123 (or 111 counting only the distinct ones).

The product of its (nonzero) digits is 486, while the sum is 24.

The square root of 193920 is about 440.3634862247. The cubic root of 193920 is about 57.8816452927.

The spelling of 193920 in words is "one hundred ninety-three thousand, nine hundred twenty".