413824 has 32 divisors (see below), whose sum is σ = 853740. Its totient is φ = 199680.

The previous prime is 413807. The next prime is 413827. The reversal of 413824 is 428314.

413824 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 2 ways, for example, as 399424 + 14400 = 632^2 + 120^2 .

It is a tau number, because it is divible by the number of its divisors (32).

Its product of digits (768) is a multiple of the sum of its prime factors (128).

It is a junction number, because it is equal to n+sod(n) for n = 413795 and 413804.

It is not an unprimeable number, because it can be changed into a prime (413827) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 6754 + ... + 6814.

2⁴¹³⁸²⁴ 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 413824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (426870).

413824 is an abundant number, since it is smaller than the sum of its proper divisors (439916).

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

413824 is an equidigital number, since it uses as much as digits as its factorization.

413824 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 128 (or 116 counting only the distinct ones).

The product of its digits is 768, while the sum is 22.

The square root of 413824 is about 643.2915357752. The cubic root of 413824 is about 74.5198361666.

The spelling of 413824 in words is "four hundred thirteen thousand, eight hundred twenty-four".