213585120 has 288 divisors, whose sum is σ = 870458400. Its totient is φ = 48771072.

The previous prime is 213585103. The next prime is 213585139. The reversal of 213585120 is 21585312.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (288).

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

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 47 ways as a sum of consecutive naturals, for example, 211176 + ... + 212184.

It is an arithmetic number, because the mean of its divisors is an integer number (3022425).

Almost surely, 2^213585120 is an apocalyptic number.

213585120 is a gapful number since it is divisible by the number (20) 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 213585120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (435229200).

213585120 is an abundant number, since it is smaller than the sum of its proper divisors (656873280).

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

213585120 is a wasteful number, since it uses less digits than its factorization.

213585120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1047 (or 1026 counting only the distinct ones).

The product of its (nonzero) digits is 2400, while the sum is 27.

The square root of 213585120 is about 14614.5516523772. The cubic root of 213585120 is about 597.7556150283.

The spelling of 213585120 in words is "two hundred thirteen million, five hundred eighty-five thousand, one hundred twenty".