102133785600 has 2112 divisors, whose sum is σ = 497096755200. Its totient is φ = 19906560000.

The previous prime is 102133785583. The next prime is 102133785623. The reversal of 102133785600 is 6587331201.

102133785600 is a `hidden beast` number, since 1 + 0 + 2 + 13 + 37 + 8 + 5 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (2112).

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

It is a congruent number.

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 191 ways as a sum of consecutive naturals, for example, 1011225550 + ... + 1011225650.

Almost surely, 2^102133785600 is an apocalyptic number.

102133785600 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 102133785600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (248548377600).

102133785600 is an abundant number, since it is smaller than the sum of its proper divisors (394962969600).

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

102133785600 is a wasteful number, since it uses less digits than its factorization.

102133785600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 177 (or 148 counting only the distinct ones).

The product of its (nonzero) digits is 30240, while the sum is 36.

The spelling of 102133785600 in words is "one hundred two billion, one hundred thirty-three million, seven hundred eighty-five thousand, six hundred".