409632 has 48 divisors (see below), whose sum is σ = 1143072. Its totient is φ = 128000.

The previous prime is 409609. The next prime is 409639. The reversal of 409632 is 236904.

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 (24).

It is an Ulam number.

It is not an unprimeable number, because it can be changed into a prime (409639) by changing a digit.

409632 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1507 + ... + 1757.

It is an arithmetic number, because the mean of its divisors is an integer number (23814).

2⁴⁰⁹⁶³² 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 409632, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (571536).

409632 is an abundant number, since it is smaller than the sum of its proper divisors (733440).

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

409632 is a wasteful number, since it uses less digits than its factorization.

409632 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 281 (or 273 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 24.

The square root of 409632 is about 640.0249995117. The cubic root of 409632 is about 74.2673552828.

It can be divided in two parts, 4096 and 32, that multiplied together give a 17-th power (131072 = 2¹⁷).

The spelling of 409632 in words is "four hundred nine thousand, six hundred thirty-two".