102125318400 has 1512 divisors, whose sum is σ = 448784400960. Its totient is φ = 22514319360.

The previous prime is 102125318353. The next prime is 102125318413. The reversal of 102125318400 is 4813521201.

102125318400 is a `hidden beast` number, since 1 + 0 + 2 + 1 + 253 + 1 + 8 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (1512).

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

It is an unprimeable number.

It is a polite number, since it can be written in 167 ways as a sum of consecutive naturals, for example, 1730937571 + ... + 1730937629.

It is an arithmetic number, because the mean of its divisors is an integer number (296815080).

Almost surely, 2^102125318400 is an apocalyptic number.

102125318400 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 102125318400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (224392200480).

102125318400 is an abundant number, since it is smaller than the sum of its proper divisors (346659082560).

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

102125318400 is an frugal number, since it uses more digits than its factorization.

102125318400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 163 (or 129 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 27.

Adding to 102125318400 its reverse (4813521201), we get a palindrome (106938839601).

The spelling of 102125318400 in words is "one hundred two billion, one hundred twenty-five million, three hundred eighteen thousand, four hundred".