165085286400 has 936 divisors, whose sum is σ = 643848181704. Its totient is φ = 40265318400.

The previous prime is 165085286341. The next prime is 165085286423. The reversal of 165085286400 is 4682580561.

165085286400 is a `hidden beast` number, since 1 + 65 + 0 + 8 + 528 + 64 + 0 + 0 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 18218520576 + 146866765824 = 134976^2 + 383232^2 .

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 71 ways as a sum of consecutive naturals, for example, 642355072 + ... + 642355328.

It is an arithmetic number, because the mean of its divisors is an integer number (687871989).

Almost surely, 2^165085286400 is an apocalyptic number.

165085286400 is a gapful number since it is divisible by the number (10) 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 165085286400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (321924090852).

165085286400 is an abundant number, since it is smaller than the sum of its proper divisors (478762895304).

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

165085286400 is a wasteful number, since it uses less digits than its factorization.

165085286400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 355 (or 325 counting only the distinct ones).

The product of its (nonzero) digits is 460800, while the sum is 45.

The spelling of 165085286400 in words is "one hundred sixty-five billion, eighty-five million, two hundred eighty-six thousand, four hundred".