413784032 has 48 divisors (see below), whose sum is σ = 843696000. Its totient is φ = 199557120.

The previous prime is 413784031. The next prime is 413784037. The reversal of 413784032 is 230487314.

It is a Harshad number since it is a multiple of its sum of digits (32).

It is a self number, because there is not a number n which added to its sum of digits gives 413784032.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413784031) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 444944 + ... + 445872.

It is an arithmetic number, because the mean of its divisors is an integer number (17577000).

Almost surely, 2^413784032 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 413784032, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (421848000).

413784032 is an abundant number, since it is smaller than the sum of its proper divisors (429911968).

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

413784032 is a wasteful number, since it uses less digits than its factorization.

413784032 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1419 (or 1411 counting only the distinct ones).

The product of its (nonzero) digits is 16128, while the sum is 32.

The square root of 413784032 is about 20341.6821329997. The cubic root of 413784032 is about 745.1743699472.

The spelling of 413784032 in words is "four hundred thirteen million, seven hundred eighty-four thousand, thirty-two".