102814249190400 has 5280 divisors, whose sum is σ = 468098469780480. Its totient is φ = 21998075904000.

The previous prime is 102814249190381. The next prime is 102814249190491. The reversal of 102814249190400 is 4091942418201.

102814249190400 is a `hidden beast` number, since 1 + 0 + 2 + 8 + 14 + 2 + 49 + 190 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (5280).

It is a Harshad number since it is a multiple of its sum of digits (45).

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 479 ways as a sum of consecutive naturals, for example, 461050444689 + ... + 461050444911.

It is an arithmetic number, because the mean of its divisors is an integer number (88655013216).

Almost surely, 2^{102814249190400} is an apocalyptic number.

102814249190400 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 102814249190400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (234049234890240).

102814249190400 is an abundant number, since it is smaller than the sum of its proper divisors (365284220590080).

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

102814249190400 is a wasteful number, since it uses less digits than its factorization.

102814249190400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 363 (or 331 counting only the distinct ones).

The product of its (nonzero) digits is 165888, while the sum is 45.

The spelling of 102814249190400 in words is "one hundred two trillion, eight hundred fourteen billion, two hundred forty-nine million, one hundred ninety thousand, four hundred".