813824 has 54 divisors (see below), whose sum is σ = 1882524. Its totient is φ = 348160.

The previous prime is 813817. The next prime is 813829. The reversal of 813824 is 428318.

It is a plaindrome in base 15.

It is a zygodrome in base 15.

It is a junction number, because it is equal to n+sod(n) for n = 813793 and 813802.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 813824.

It is not an unprimeable number, because it can be changed into a prime (813829) by changing a digit.

813824 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 5 ways as a sum of consecutive naturals, for example, 47864 + ... + 47880.

2⁸¹³⁸²⁴ 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 813824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (941262).

813824 is an abundant number, since it is smaller than the sum of its proper divisors (1068700).

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

813824 is a wasteful number, since it uses less digits than its factorization.

813824 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 61 (or 30 counting only the distinct ones).

The product of its digits is 1536, while the sum is 26.

The square root of 813824 is about 902.1219429767. The cubic root of 813824 is about 93.3634370014.

It can be divided in two parts, 8 and 13824, that multiplied together give a cube (110592 = 48³).

The spelling of 813824 in words is "eight hundred thirteen thousand, eight hundred twenty-four".