164216728166400 has 6048 divisors, whose sum is σ = 806073922967040. Its totient is φ = 32197029396480.

The previous prime is 164216728166371. The next prime is 164216728166423. The reversal of 164216728166400 is 4661827612461.

164216728166400 is a `hidden beast` number, since 1 + 6 + 4 + 2 + 1 + 6 + 72 + 8 + 166 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (6048).

It is a super-2 number, since 2×164216728166400² (a number of 29 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

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 431 ways as a sum of consecutive naturals, for example, 2078692761561 + ... + 2078692761639.

It is an arithmetic number, because the mean of its divisors is an integer number (133279418480).

Almost surely, 2^{164216728166400} is an apocalyptic number.

164216728166400 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 164216728166400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (403036961483520).

164216728166400 is an abundant number, since it is smaller than the sum of its proper divisors (641857194800640).

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

164216728166400 is an frugal number, since it uses more digits than its factorization.

164216728166400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 176 (or 126 counting only the distinct ones).

The product of its (nonzero) digits is 4644864, while the sum is 54.

The spelling of 164216728166400 in words is "one hundred sixty-four trillion, two hundred sixteen billion, seven hundred twenty-eight million, one hundred sixty-six thousand, four hundred".