10205625830400 has 6336 divisors, whose sum is σ = 55081244574720. Its totient is φ = 1732666982400.

The previous prime is 10205625830363. The next prime is 10205625830471. The reversal of 10205625830400 is 403852650201.

10205625830400 is a `hidden beast` number, since 1 + 0 + 2 + 0 + 562 + 58 + 3 + 0 + 40 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (6336).

It is a Harshad number since it is a multiple of its sum of digits (36).

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 575 ways as a sum of consecutive naturals, for example, 74493619132 + ... + 74493619268.

Almost surely, 2^{10205625830400} is an apocalyptic number.

10205625830400 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 10205625830400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (27540622287360).

10205625830400 is an abundant number, since it is smaller than the sum of its proper divisors (44875618744320).

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

10205625830400 is a wasteful number, since it uses less digits than its factorization.

10205625830400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 240 (or 214 counting only the distinct ones).

The product of its (nonzero) digits is 57600, while the sum is 36.

The spelling of 10205625830400 in words is "ten trillion, two hundred five billion, six hundred twenty-five million, eight hundred thirty thousand, four hundred".