90434664658800 has 2160 divisors, whose sum is σ = 435781122910560. Its totient is φ = 17686016409600.

The previous prime is 90434664658777. The next prime is 90434664658831. The reversal of 90434664658800 is 885646643409.

90434664658800 is a `hidden beast` number, since 9 + 0 + 4 + 3 + 4 + 6 + 6 + 46 + 588 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2160).

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (29) of ones.

It is a polite number, since it can be written in 431 ways as a sum of consecutive naturals, for example, 1088522862 + ... + 1088605938.

It is an arithmetic number, because the mean of its divisors is an integer number (201750519866).

Almost surely, 2^{90434664658800} is an apocalyptic number.

90434664658800 is a gapful number since it is divisible by the number (90) 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 90434664658800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (217890561455280).

90434664658800 is an abundant number, since it is smaller than the sum of its proper divisors (345346458251760).

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

90434664658800 is a wasteful number, since it uses less digits than its factorization.

90434664658800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 83157 (or 83122 counting only the distinct ones).

The product of its (nonzero) digits is 119439360, while the sum is 63.

The spelling of 90434664658800 in words is "ninety trillion, four hundred thirty-four billion, six hundred sixty-four million, six hundred fifty-eight thousand, eight hundred".