4116589171200 has 960 divisors, whose sum is σ = 16518261513600. Its totient is φ = 995858841600.

The previous prime is 4116589171157. The next prime is 4116589171223. The reversal of 4116589171200 is 21719856114.

4116589171200 is a `hidden beast` number, since 41 + 1 + 6 + 589 + 1 + 7 + 1 + 20 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (960).

It is a super-2 number, since 2×4116589171200² (a number of 26 digits) contains 22 as substring.

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

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 95 ways as a sum of consecutive naturals, for example, 2558475996 + ... + 2558477604.

It is an arithmetic number, because the mean of its divisors is an integer number (17206522410).

Almost surely, 2^{4116589171200} is an apocalyptic number.

4116589171200 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 4116589171200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8259130756800).

4116589171200 is an abundant number, since it is smaller than the sum of its proper divisors (12401672342400).

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

4116589171200 is a wasteful number, since it uses less digits than its factorization.

4116589171200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2330 (or 2303 counting only the distinct ones).

The product of its (nonzero) digits is 120960, while the sum is 45.

The spelling of 4116589171200 in words is "four trillion, one hundred sixteen billion, five hundred eighty-nine million, one hundred seventy-one thousand, two hundred".