193952 has 48 divisors (see below), whose sum is σ = 453600. Its totient is φ = 80640.

The previous prime is 193951. The next prime is 193957. The reversal of 193952 is 259391.

193952 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (29).

It is not an unprimeable number, because it can be changed into a prime (193951) 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, 6674 + ... + 6702.

It is an arithmetic number, because the mean of its divisors is an integer number (9450).

2¹⁹³⁹⁵² 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 193952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (226800).

193952 is an abundant number, since it is smaller than the sum of its proper divisors (259648).

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

193952 is a wasteful number, since it uses less digits than its factorization.

193952 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 69 (or 61 counting only the distinct ones).

The product of its digits is 2430, while the sum is 29.

The square root of 193952 is about 440.3998183469. The cubic root of 193952 is about 57.8848289265.

It can be divided in two parts, 1939 and 52, that added together give a palindrome (1991).

The spelling of 193952 in words is "one hundred ninety-three thousand, nine hundred fifty-two".