90198086284800 has 2400 divisors, whose sum is σ = 387278465925120. Its totient is φ = 20542375526400.

The previous prime is 90198086284799. The next prime is 90198086284811. The reversal of 90198086284800 is 848268089109.

90198086284800 is a `hidden beast` number, since 9 + 0 + 1 + 98 + 0 + 8 + 62 + 8 + 480 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2400).

It is a super-2 number, since 2×90198086284800² (a number of 29 digits) contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 11011848705 + ... + 11011856895.

Almost surely, 2^{90198086284800} is an apocalyptic number.

90198086284800 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 90198086284800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (193639232962560).

90198086284800 is an abundant number, since it is smaller than the sum of its proper divisors (297080379640320).

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

90198086284800 is a wasteful number, since it uses less digits than its factorization.

90198086284800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 8306 (or 8276 counting only the distinct ones).

The product of its (nonzero) digits is 15925248, while the sum is 63.

The spelling of 90198086284800 in words is "ninety trillion, one hundred ninety-eight billion, eighty-six million, two hundred eighty-four thousand, eight hundred".