189315584640000 has 5775 divisors, whose sum is σ = 895680742987833. Its totient is φ = 39943507968000.

The previous prime is 189315584639977. The next prime is 189315584640053. The reversal of 189315584640000 is 46485513981.

It is a happy number.

The square root of 189315584640000 is 13759200.

It is a perfect power (a square), and thus also a powerful number.

189315584640000 is a `hidden beast` number, since 1 + 8 + 9 + 3 + 1 + 558 + 46 + 40 + 0 + 0 + 0 = 666.

It can be written as a sum of positive squares in 7 ways, for example, as 186992716022784 + 2322868617216 = 13674528^2 + 1524096^2 .

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 524 ways as a sum of consecutive naturals, for example, 14562737279994 + ... + 14562737280006.

Almost surely, 2^{189315584640000} is an apocalyptic number.

189315584640000 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

189315584640000 is the 13759200-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 189315584640000

189315584640000 is an abundant number, since it is smaller than the sum of its proper divisors (706365158347833).

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

189315584640000 is an frugal number, since it uses more digits than its factorization.

189315584640000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 112 (or 30 counting only the distinct ones).

The product of its (nonzero) digits is 4147200, while the sum is 54.

The spelling of 189315584640000 in words is "one hundred eighty-nine trillion, three hundred fifteen billion, five hundred eighty-four million, six hundred forty thousand".