90135077760 has 768 divisors, whose sum is σ = 384943104000. Its totient is φ = 18924945408.

The previous prime is 90135077713. The next prime is 90135077777. The reversal of 90135077760 is 6777053109.

90135077760 is a `hidden beast` number, since 9 + 0 + 13 + 507 + 77 + 60 = 666.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 188173201 + ... + 188173679.

It is an arithmetic number, because the mean of its divisors is an integer number (501228000).

Almost surely, 2^90135077760 is an apocalyptic number.

90135077760 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 90135077760, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (192471552000).

90135077760 is an abundant number, since it is smaller than the sum of its proper divisors (294808026240).

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

90135077760 is a wasteful number, since it uses less digits than its factorization.

90135077760 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 883 (or 868 counting only the distinct ones).

The product of its (nonzero) digits is 277830, while the sum is 45.

The spelling of 90135077760 in words is "ninety billion, one hundred thirty-five million, seventy-seven thousand, seven hundred sixty".