102972928838400 has 1296 divisors, whose sum is σ = 415742153299200. Its totient is φ = 25116962734080.

The previous prime is 102972928838357. The next prime is 102972928838449. The reversal of 102972928838400 is 4838829279201.

102972928838400 is a `hidden beast` number, since 1 + 0 + 2 + 97 + 2 + 92 + 88 + 384 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1296).

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 143 ways as a sum of consecutive naturals, for example, 856855117 + ... + 856975283.

Almost surely, 2^{102972928838400} is an apocalyptic number.

102972928838400 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 102972928838400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (207871076649600).

102972928838400 is an abundant number, since it is smaller than the sum of its proper divisors (312769224460800).

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

102972928838400 is a wasteful number, since it uses less digits than its factorization.

102972928838400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 120256 (or 120225 counting only the distinct ones).

The product of its (nonzero) digits is 27869184, while the sum is 63.

The spelling of 102972928838400 in words is "one hundred two trillion, nine hundred seventy-two billion, nine hundred twenty-eight million, eight hundred thirty-eight thousand, four hundred".