4164166389600 has 2016 divisors, whose sum is σ = 17969819232960. Its totient is φ = 922310737920.

The previous prime is 4164166389599. The next prime is 4164166389611. The reversal of 4164166389600 is 69836614614.

4164166389600 is a `hidden beast` number, since 4 + 16 + 4 + 16 + 6 + 3 + 8 + 9 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (2016).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 335 ways as a sum of consecutive naturals, for example, 26523352722 + ... + 26523352878.

It is an arithmetic number, because the mean of its divisors is an integer number (8913600810).

Almost surely, 2^{4164166389600} is an apocalyptic number.

4164166389600 is a gapful number since it is divisible by the number (40) 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 4164166389600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8984909616480).

4164166389600 is an abundant number, since it is smaller than the sum of its proper divisors (13805652843360).

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

4164166389600 is a wasteful number, since it uses less digits than its factorization.

4164166389600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 364 (or 336 counting only the distinct ones).

The product of its (nonzero) digits is 4478976, while the sum is 54.

The spelling of 4164166389600 in words is "four trillion, one hundred sixty-four billion, one hundred sixty-six million, three hundred eighty-nine thousand, six hundred".