165484800 has 486 divisors, whose sum is σ = 678343302. Its totient is φ = 38338560.

The previous prime is 165484799. The next prime is 165484801. The reversal of 165484800 is 8484561.

It is an interprime number because it is at equal distance from previous prime (165484799) and next prime (165484801).

It can be written as a sum of positive squares in 9 ways, for example, as 81432576 + 84052224 = 9024^2 + 9168^2 .

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

It is not an unprimeable number, because it can be changed into a prime (165484801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 9734392 + ... + 9734408.

Almost surely, 2^165484800 is an apocalyptic number.

165484800 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 165484800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (339171651).

165484800 is an abundant number, since it is smaller than the sum of its proper divisors (512858502).

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

165484800 is a wasteful number, since it uses less digits than its factorization.

165484800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 75 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 30720, while the sum is 36.

The square root of 165484800 is about 12864.0895519271. The cubic root of 165484800 is about 549.0173086205.

The spelling of 165484800 in words is "one hundred sixty-five million, four hundred eighty-four thousand, eight hundred".