821408 has 48 divisors (see below), whose sum is σ = 1955520. Its totient is φ = 331776.

The previous prime is 821383. The next prime is 821411. The reversal of 821408 is 804128.

It is a super-2 number, since 2×821408² = 1349422204928, which contains 22 as substring.

It is an unprimeable number.

821408 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 4160 + ... + 4352.

It is an arithmetic number, because the mean of its divisors is an integer number (40740).

2⁸²¹⁴⁰⁸ 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 821408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (977760).

821408 is an abundant number, since it is smaller than the sum of its proper divisors (1134112).

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

821408 is a wasteful number, since it uses less digits than its factorization.

821408 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 229 (or 221 counting only the distinct ones).

The product of its (nonzero) digits is 512, while the sum is 23.

The square root of 821408 is about 906.3156183141. The cubic root of 821408 is about 93.6525577181.

The spelling of 821408 in words is "eight hundred twenty-one thousand, four hundred eight".