90145716998400 has 1296 divisors, whose sum is σ = 404444794126464. Its totient is φ = 19392652247040.

The previous prime is 90145716998339. The next prime is 90145716998471. The reversal of 90145716998400 is 489961754109.

90145716998400 is a `hidden beast` number, since 9 + 0 + 1 + 457 + 16 + 99 + 84 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1296).

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

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 184825254 + ... + 185312346.

Almost surely, 2^{90145716998400} is an apocalyptic number.

90145716998400 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 90145716998400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (202222397063232).

90145716998400 is an abundant number, since it is smaller than the sum of its proper divisors (314299077128064).

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

90145716998400 is a wasteful number, since it uses less digits than its factorization.

90145716998400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 487158 (or 487127 counting only the distinct ones).

The product of its (nonzero) digits is 19595520, while the sum is 63.

The spelling of 90145716998400 in words is "ninety trillion, one hundred forty-five billion, seven hundred sixteen million, nine hundred ninety-eight thousand, four hundred".