413784 has 48 divisors (see below), whose sum is σ = 1282320. Its totient is φ = 118080.

The previous prime is 413783. The next prime is 413807. The reversal of 413784 is 487314.

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413783) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 94 + ... + 914.

It is an arithmetic number, because the mean of its divisors is an integer number (26715).

2⁴¹³⁷⁸⁴ 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 413784, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (641160).

413784 is an abundant number, since it is smaller than the sum of its proper divisors (868536).

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

413784 is a wasteful number, since it uses less digits than its factorization.

413784 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 840 (or 833 counting only the distinct ones).

The product of its digits is 2688, while the sum is 27.

The square root of 413784 is about 643.2604449210. The cubic root of 413784 is about 74.5174350738.

The spelling of 413784 in words is "four hundred thirteen thousand, seven hundred eighty-four".