189993600 has 240 divisors, whose sum is σ = 702074670. Its totient is φ = 50595840.

The previous prime is 189993577. The next prime is 189993607. The reversal of 189993600 is 6399981.

It can be written as a sum of positive squares in 3 ways, for example, as 181279296 + 8714304 = 13464^2 + 2952^2 .

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (189993607) by changing a digit.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 258834 + ... + 259566.

Almost surely, 2^189993600 is an apocalyptic number.

189993600 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 189993600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (351037335).

189993600 is an abundant number, since it is smaller than the sum of its proper divisors (512081070).

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

189993600 is an equidigital number, since it uses as much as digits as its factorization.

189993600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 769 (or 743 counting only the distinct ones).

The product of its (nonzero) digits is 104976, while the sum is 45.

The square root of 189993600 is about 13783.8165977352. The cubic root of 189993600 is about 574.8832529200.

The spelling of 189993600 in words is "one hundred eighty-nine million, nine hundred ninety-three thousand, six hundred".