102864000 has 128 divisors (see below), whose sum is σ = 341153280. Its totient is φ = 27417600.

The previous prime is 102863989. The next prime is 102864001. The reversal of 102864000 is 468201.

It is a tau number, because it is divible by the number of its divisors (128).

It is not an unprimeable number, because it can be changed into a prime (102864001) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 46929 + ... + 49071.

It is an arithmetic number, because the mean of its divisors is an integer number (2665260).

Almost surely, 2^102864000 is an apocalyptic number.

102864000 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 102864000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (170576640).

102864000 is an abundant number, since it is smaller than the sum of its proper divisors (238289280).

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

102864000 is an equidigital number, since it uses as much as digits as its factorization.

102864000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2175 (or 2153 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 21.

The square root of 102864000 is about 10142.1891128099. The cubic root of 102864000 is about 468.5484110956.

The spelling of 102864000 in words is "one hundred two million, eight hundred sixty-four thousand".