821424 has 40 divisors (see below), whose sum is σ = 2155120. Its totient is φ = 269568.

The previous prime is 821411. The next prime is 821441. The reversal of 821424 is 424128.

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

It is a self number, because there is not a number n which added to its sum of digits gives 821424.

It is a congruent number.

It is an unprimeable number.

821424 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 7 ways as a sum of consecutive naturals, for example, 5154 + ... + 5310.

It is an arithmetic number, because the mean of its divisors is an integer number (53878).

2⁸²¹⁴²⁴ 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 821424, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1077560).

821424 is an abundant number, since it is smaller than the sum of its proper divisors (1333696).

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

821424 is a wasteful number, since it uses less digits than its factorization.

821424 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 277 (or 271 counting only the distinct ones).

The product of its digits is 512, while the sum is 21.

The square root of 821424 is about 906.3244452182. The cubic root of 821424 is about 93.6531657923.

It can be divided in two parts, 8214 and 24, that multiplied together give a square (197136 = 444²).

The spelling of 821424 in words is "eight hundred twenty-one thousand, four hundred twenty-four".