165888000 has 300 divisors, whose sum is σ = 618509892. Its totient is φ = 44236800.

The previous prime is 165887977. The next prime is 165888011. The reversal of 165888000 is 888561.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Jordan-Polya number, since it can be written as 6! ⋅ (5!)² ⋅ (2!)⁴.

It can be written as a sum of positive squares in 2 ways, for example, as 5308416 + 160579584 = 2304^2 + 12672^2 .

It is a tau number, because it is divible by the number of its divisors (300).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 33177598 + ... + 33177602.

Almost surely, 2^165888000 is an apocalyptic number.

165888000 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 165888000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (309254946).

165888000 is an abundant number, since it is smaller than the sum of its proper divisors (452621892).

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

165888000 is an frugal number, since it uses more digits than its factorization.

165888000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 55 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 15360, while the sum is 36.

The square root of 165888000 is about 12879.7515503988. The cubic root of 165888000 is about 549.4628364256.

The spelling of 165888000 in words is "one hundred sixty-five million, eight hundred eighty-eight thousand".