10185806400 has 1008 divisors, whose sum is σ = 44120604672. Its totient is φ = 2032128000.

The previous prime is 10185806363. The next prime is 10185806429. The reversal of 10185806400 is 460858101.

It is a hoax number, since the sum of its digits (33) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (33).

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 80203137 + ... + 80203263.

Almost surely, 2^10185806400 is an apocalyptic number.

10185806400 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 10185806400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (22060302336).

10185806400 is an abundant number, since it is smaller than the sum of its proper divisors (33934798272).

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

10185806400 is a wasteful number, since it uses less digits than its factorization.

10185806400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 208 (or 186 counting only the distinct ones).

The product of its (nonzero) digits is 7680, while the sum is 33.

The spelling of 10185806400 in words is "ten billion, one hundred eighty-five million, eight hundred six thousand, four hundred".