27729821750400 has 1728 divisors, whose sum is σ = 130217089635360. Its totient is φ = 5761953792000.

The previous prime is 27729821750387. The next prime is 27729821750401. The reversal of 27729821750400 is 405712892772.

27729821750400 is a `hidden beast` number, since 2 + 77 + 29 + 82 + 1 + 75 + 0 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (1728).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (27729821750401) by changing a digit.

It is a polite number, since it can be written in 215 ways as a sum of consecutive naturals, for example, 419093320 + ... + 419159480.

Almost surely, 2^{27729821750400} is an apocalyptic number.

27729821750400 is a gapful number since it is divisible by the number (20) 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 27729821750400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (65108544817680).

27729821750400 is an abundant number, since it is smaller than the sum of its proper divisors (102487267884960).

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

27729821750400 is a wasteful number, since it uses less digits than its factorization.

27729821750400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 66225 (or 66189 counting only the distinct ones).

The product of its (nonzero) digits is 3951360, while the sum is 54.

The spelling of 27729821750400 in words is "twenty-seven trillion, seven hundred twenty-nine billion, eight hundred twenty-one million, seven hundred fifty thousand, four hundred".