90181324800 has 702 divisors, whose sum is σ = 375934611078. Its totient is φ = 20602552320.

The previous prime is 90181324789. The next prime is 90181324813. The reversal of 90181324800 is 842318109.

It can be written as a sum of positive squares in 3 ways, for example, as 354041856 + 89827282944 = 18816^2 + 299712^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 45157402 + ... + 45159398.

It is an arithmetic number, because the mean of its divisors is an integer number (535519389).

Almost surely, 2^90181324800 is an apocalyptic number.

90181324800 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 90181324800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (187967305539).

90181324800 is an abundant number, since it is smaller than the sum of its proper divisors (285753286278).

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

90181324800 is a wasteful number, since it uses less digits than its factorization.

90181324800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2051 (or 2014 counting only the distinct ones).

The product of its (nonzero) digits is 13824, while the sum is 36.

The spelling of 90181324800 in words is "ninety billion, one hundred eighty-one million, three hundred twenty-four thousand, eight hundred".