90509506560 has 1152 divisors, whose sum is σ = 372866457600. Its totient is φ = 20065812480.

The previous prime is 90509506553. The next prime is 90509506561. The reversal of 90509506560 is 6560590509.

90509506560 is a `hidden beast` number, since 90 + 5 + 0 + 9 + 506 + 56 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (90509506561) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 712673217 + ... + 712673343.

It is an arithmetic number, because the mean of its divisors is an integer number (323668800).

Almost surely, 2^90509506560 is an apocalyptic number.

90509506560 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 90509506560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (186433228800).

90509506560 is an abundant number, since it is smaller than the sum of its proper divisors (282356951040).

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

90509506560 is a wasteful number, since it uses less digits than its factorization.

90509506560 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 227 (or 204 counting only the distinct ones).

The product of its (nonzero) digits is 364500, while the sum is 45.

The spelling of 90509506560 in words is "ninety billion, five hundred nine million, five hundred six thousand, five hundred sixty".