164032416288000 has 1728 divisors, whose sum is σ = 676965614375232. Its totient is φ = 37779878707200.

The previous prime is 164032416287969. The next prime is 164032416288023. The reversal of 164032416288000 is 882614230461.

164032416288000 is a `hidden beast` number, since 1 + 6 + 40 + 324 + 1 + 6 + 288 + 0 + 0 + 0 = 666.

It can be written as a sum of positive squares in 32 ways, for example, as 106543023393024 + 57489392894976 = 10321968^2 + 7582176^2 .

It is a super-3 number, since 3×164032416288000³ (a number of 44 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 an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 11011096552 + ... + 11011111448.

It is an arithmetic number, because the mean of its divisors is an integer number (391762508319).

Almost surely, 2^{164032416288000} is an apocalyptic number.

164032416288000 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 164032416288000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (338482807187616).

164032416288000 is an abundant number, since it is smaller than the sum of its proper divisors (512933198087232).

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

164032416288000 is a wasteful number, since it uses less digits than its factorization.

164032416288000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 15137 (or 15110 counting only the distinct ones).

The product of its (nonzero) digits is 442368, while the sum is 45.

The spelling of 164032416288000 in words is "one hundred sixty-four trillion, thirty-two billion, four hundred sixteen million, two hundred eighty-eight thousand".