193568 has 24 divisors (see below), whose sum is σ = 399168. Its totient is φ = 92224.

The previous prime is 193559. The next prime is 193573. The reversal of 193568 is 865391.

It is a Harshad number since it is a multiple of its sum of digits (32).

It is an unprimeable number.

193568 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 605 + ... + 867.

It is an arithmetic number, because the mean of its divisors is an integer number (16632).

2¹⁹³⁵⁶⁸ 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 193568, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (199584).

193568 is an abundant number, since it is smaller than the sum of its proper divisors (205600).

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

193568 is a wasteful number, since it uses less digits than its factorization.

193568 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 296 (or 288 counting only the distinct ones).

The product of its digits is 6480, while the sum is 32.

The square root of 193568 is about 439.9636348609. The cubic root of 193568 is about 57.8466021834.

Adding to 193568 its sum of digits (32), we get a square (193600 = 440²).

The spelling of 193568 in words is "one hundred ninety-three thousand, five hundred sixty-eight".