193072000 has 128 divisors (see below), whose sum is σ = 524141280. Its totient is φ = 70144000.

The previous prime is 193071953. The next prime is 193072003. The reversal of 193072000 is 270391.

It is a tau number, because it is divible by the number of its divisors (128).

It is a Harshad number since it is a multiple of its sum of digits (22).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (193072003) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 175452 + ... + 176548.

Almost surely, 2^193072000 is an apocalyptic number.

193072000 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 193072000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (262070640).

193072000 is an abundant number, since it is smaller than the sum of its proper divisors (331069280).

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

193072000 is a wasteful number, since it uses less digits than its factorization.

193072000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1137 (or 1115 counting only the distinct ones).

The product of its (nonzero) digits is 378, while the sum is 22.

The square root of 193072000 is about 13895.0350845185. The cubic root of 193072000 is about 577.9715107504.

The spelling of 193072000 in words is "one hundred ninety-three million, seventy-two thousand".