102066585600 has 768 divisors, whose sum is σ = 409567536000. Its totient is φ = 21894266880.

The previous prime is 102066585589. The next prime is 102066585601. The reversal of 102066585600 is 6585660201.

It is a tau number, because it is divible by the number of its divisors (768).

It is not an unprimeable number, because it can be changed into a prime (102066585601) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 292454226 + ... + 292454574.

Almost surely, 2^102066585600 is an apocalyptic number.

102066585600 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 102066585600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (204783768000).

102066585600 is an abundant number, since it is smaller than the sum of its proper divisors (307500950400).

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

102066585600 is an equidigital number, since it uses as much as digits as its factorization.

102066585600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 416 (or 383 counting only the distinct ones).

The product of its (nonzero) digits is 86400, while the sum is 39.

It can be divided in two parts, 1020 and 66585600, that multiplied together give a cube (67917312000 = 4080³).

The spelling of 102066585600 in words is "one hundred two billion, sixty-six million, five hundred eighty-five thousand, six hundred".