90105735096000 has 1792 divisors, whose sum is σ = 376480595312640. Its totient is φ = 20940042240000.

The previous prime is 90105735095939. The next prime is 90105735096019. The reversal of 90105735096000 is 69053750109.

90105735096000 is a `hidden beast` number, since 9 + 0 + 1 + 0 + 5 + 7 + 35 + 0 + 9 + 600 + 0 = 666.

It is a super-2 number, since 2×90105735096000² (a number of 29 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 polite number, since it can be written in 255 ways as a sum of consecutive naturals, for example, 3568955377 + ... + 3568980623.

It is an arithmetic number, because the mean of its divisors is an integer number (210089617920).

Almost surely, 2^{90105735096000} is an apocalyptic number.

90105735096000 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 90105735096000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (188240297656320).

90105735096000 is an abundant number, since it is smaller than the sum of its proper divisors (286374860216640).

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

90105735096000 is a wasteful number, since it uses less digits than its factorization.

90105735096000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 25368 (or 25342 counting only the distinct ones).

The product of its (nonzero) digits is 255150, while the sum is 45.

The spelling of 90105735096000 in words is "ninety trillion, one hundred five billion, seven hundred thirty-five million, ninety-six thousand".