205032416400 has 420 divisors, whose sum is σ = 844062936832. Its totient is φ = 46864085760.

The previous prime is 205032416293. The next prime is 205032416429. The reversal of 205032416400 is 4614230502.

205032416400 is a `hidden beast` number, since 205 + 0 + 3 + 2 + 416 + 40 + 0 = 666.

205032416400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (420).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 83 ways as a sum of consecutive naturals, for example, 1990977 + ... + 2091423.

Almost surely, 2^205032416400 is an apocalyptic number.

205032416400 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 205032416400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (422031468416).

205032416400 is an abundant number, since it is smaller than the sum of its proper divisors (639030520432).

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

205032416400 is a wasteful number, since it uses less digits than its factorization.

205032416400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 100490 (or 100464 counting only the distinct ones).

The product of its (nonzero) digits is 5760, while the sum is 27.

Adding to 205032416400 its reverse (4614230502), we get a palindrome (209646646902).

The spelling of 205032416400 in words is "two hundred five billion, thirty-two million, four hundred sixteen thousand, four hundred".