193968 has 40 divisors (see below), whose sum is σ = 558000. Its totient is φ = 64512.

The previous prime is 193957. The next prime is 193979. The reversal of 193968 is 869391.

It is an interprime number because it is at equal distance from previous prime (193957) and next prime (193979).

It is a Harshad number since it is a multiple of its sum of digits (36).

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

It is a nialpdrome in base 12.

It is an unprimeable number.

193968 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 7 ways as a sum of consecutive naturals, for example, 208 + ... + 656.

It is an arithmetic number, because the mean of its divisors is an integer number (13950).

193968 is a Friedman number, since it can be written as 6^3*(899-1), using all its digits and the basic arithmetic operations.

2¹⁹³⁹⁶⁸ is an apocalyptic number.

193968 is a gapful number since it is divisible by the number (18) 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 193968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (279000).

193968 is an abundant number, since it is smaller than the sum of its proper divisors (364032).

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

193968 is a wasteful number, since it uses less digits than its factorization.

193968 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 466 (or 454 counting only the distinct ones).

The product of its digits is 11664, while the sum is 36.

The square root of 193968 is about 440.4179832841. The cubic root of 193968 is about 57.8864206121.

The spelling of 193968 in words is "one hundred ninety-three thousand, nine hundred sixty-eight".