101564668800 has 1152 divisors, whose sum is σ = 439761853440. Its totient is φ = 22663618560.

The previous prime is 101564668769. The next prime is 101564668817. The reversal of 101564668800 is 8866465101.

101564668800 is a `hidden beast` number, since 1 + 0 + 1 + 564 + 6 + 6 + 8 + 80 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 255830202 + ... + 255830598.

It is an arithmetic number, because the mean of its divisors is an integer number (381737720).

Almost surely, 2^101564668800 is an apocalyptic number.

101564668800 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 101564668800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (219880926720).

101564668800 is an abundant number, since it is smaller than the sum of its proper divisors (338197184640).

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

101564668800 is an equidigital number, since it uses as much as digits as its factorization.

101564668800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 490 (or 461 counting only the distinct ones).

The product of its (nonzero) digits is 276480, while the sum is 45.

The spelling of 101564668800 in words is "one hundred one billion, five hundred sixty-four million, six hundred sixty-eight thousand, eight hundred".