209952 has 54 divisors (see below), whose sum is σ = 619983. Its totient is φ = 69984.

The previous prime is 209939. The next prime is 209953. The reversal of 209952 is 259902.

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 can be written as a sum of positive squares in only one way, i.e., 104976 + 104976 = 324^2 + 324^2 .

It is a tau number, because it is divible by the number of its divisors (54).

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=324.

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

It is a nialpdrome in base 6.

It is not an unprimeable number, because it can be changed into a prime (209953) by changing a digit.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 69983 + 69984 + 69985.

209952 is a Friedman number, since it can be written as (9*9)^2*(2+0)^5, using all its digits and the basic arithmetic operations.

2²⁰⁹⁹⁵² 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 209952

209952 is an abundant number, since it is smaller than the sum of its proper divisors (410031).

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

209952 is an frugal number, since it uses more digits than its factorization.

209952 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 34 (or 5 counting only the distinct ones).

The product of its (nonzero) digits is 1620, while the sum is 27.

The square root of 209952 is about 458.2051942089. The cubic root of 209952 is about 59.4346904801.

209952 divided by its sum of digits (27) gives a 5-th power (7776 = 6⁵).

The spelling of 209952 in words is "two hundred nine thousand, nine hundred fifty-two".