409752 has 64 divisors (see below), whose sum is σ = 1305600. Its totient is φ = 116640.

The previous prime is 409733. The next prime is 409753. The reversal of 409752 is 257904.

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

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 409752.

It is not an unprimeable number, because it can be changed into a prime (409753) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1377 + ... + 1647.

It is an arithmetic number, because the mean of its divisors is an integer number (20400).

2⁴⁰⁹⁷⁵² is an apocalyptic number.

409752 is a gapful number since it is divisible by the number (42) 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 409752, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (652800).

409752 is an abundant number, since it is smaller than the sum of its proper divisors (895848).

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

409752 is a wasteful number, since it uses less digits than its factorization.

409752 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 293 (or 283 counting only the distinct ones).

The product of its (nonzero) digits is 2520, while the sum is 27.

The square root of 409752 is about 640.1187389852. The cubic root of 409752 is about 74.2746066796.

The spelling of 409752 in words is "four hundred nine thousand, seven hundred fifty-two".