409952 has 24 divisors (see below), whose sum is σ = 843696. Its totient is φ = 195712.

The previous prime is 409951. The next prime is 409961. The reversal of 409952 is 259904.

409952 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a plaindrome in base 13.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (409951) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 458 + ... + 1014.

It is an arithmetic number, because the mean of its divisors is an integer number (35154).

2⁴⁰⁹⁹⁵² 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 409952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (421848).

409952 is an abundant number, since it is smaller than the sum of its proper divisors (433744).

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

409952 is a wasteful number, since it uses less digits than its factorization.

409952 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 590 (or 582 counting only the distinct ones).

The product of its (nonzero) digits is 3240, while the sum is 29.

The square root of 409952 is about 640.2749409433. The cubic root of 409952 is about 74.2866891954.

The spelling of 409952 in words is "four hundred nine thousand, nine hundred fifty-two".