102007382400 has 1920 divisors, whose sum is σ = 495852192000. Its totient is φ = 20006092800.

The previous prime is 102007382377. The next prime is 102007382447. The reversal of 102007382400 is 4283700201.

It is a tau number, because it is divible by the number of its divisors (1920).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 379209466 + ... + 379209734.

It is an arithmetic number, because the mean of its divisors is an integer number (258256350).

Almost surely, 2^102007382400 is an apocalyptic number.

102007382400 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 102007382400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (247926096000).

102007382400 is an abundant number, since it is smaller than the sum of its proper divisors (393844809600).

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

102007382400 is a wasteful number, since it uses less digits than its factorization.

102007382400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 342 (or 316 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

The spelling of 102007382400 in words is "one hundred two billion, seven million, three hundred eighty-two thousand, four hundred".