208512 has 48 divisors (see below), whose sum is σ = 603330. Its totient is φ = 69120.

The previous prime is 208511. The next prime is 208513. The reversal of 208512 is 215802.

It is an interprime number because it is at equal distance from previous prime (208511) and next prime (208513).

It can be written as a sum of positive squares in only one way, i.e., 207936 + 576 = 456^2 + 24^2 .

It is a tau number, because it is divible by the number of its divisors (48).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 208512.

It is not an unprimeable number, because it can be changed into a prime (208511) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 1062 + ... + 1242.

2²⁰⁸⁵¹² is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 208512, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (301665).

208512 is an abundant number, since it is smaller than the sum of its proper divisors (394818).

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

208512 is a wasteful number, since it uses less digits than its factorization.

208512 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 201 (or 186 counting only the distinct ones).

The product of its (nonzero) digits is 160, while the sum is 18.

The square root of 208512 is about 456.6311421706. The cubic root of 208512 is about 59.2984968532.

The spelling of 208512 in words is "two hundred eight thousand, five hundred twelve".