101664009064800 has 2592 divisors, whose sum is σ = 474604437434400. Its totient is φ = 20240830955520.

The previous prime is 101664009064777. The next prime is 101664009064801. The reversal of 101664009064800 is 8460900466101.

101664009064800 is a `hidden beast` number, since 1 + 0 + 166 + 4 + 0 + 0 + 9 + 0 + 6 + 480 + 0 = 666.

It is a super-3 number, since 3×101664009064800³ (a number of 43 digits) contains 333 as substring.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (101664009064801) by changing a digit.

It is a polite number, since it can be written in 431 ways as a sum of consecutive naturals, for example, 23441088232 + ... + 23441092568.

It is an arithmetic number, because the mean of its divisors is an integer number (183103563825).

Almost surely, 2^{101664009064800} is an apocalyptic number.

101664009064800 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 101664009064800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (237302218717200).

101664009064800 is an abundant number, since it is smaller than the sum of its proper divisors (372940428369600).

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

101664009064800 is a wasteful number, since it uses less digits than its factorization.

101664009064800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 4678 (or 4655 counting only the distinct ones).

The product of its (nonzero) digits is 248832, while the sum is 45.

The spelling of 101664009064800 in words is "one hundred one trillion, six hundred sixty-four billion, nine million, sixty-four thousand, eight hundred".