821664 has 60 divisors (see below), whose sum is σ = 2424114. Its totient is φ = 273024.

The previous prime is 821663. The next prime is 821677. The reversal of 821664 is 466128.

It can be written as a sum of positive squares in only one way, i.e., 810000 + 11664 = 900^2 + 108^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

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

It is not an unprimeable number, because it can be changed into a prime (821663) 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 9 ways as a sum of consecutive naturals, for example, 2434 + ... + 2750.

2⁸²¹⁶⁶⁴ 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 821664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1212057).

821664 is an abundant number, since it is smaller than the sum of its proper divisors (1602450).

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

821664 is a wasteful number, since it uses less digits than its factorization.

821664 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 339 (or 322 counting only the distinct ones).

The product of its digits is 2304, while the sum is 27.

The square root of 821664 is about 906.4568384650. The cubic root of 821664 is about 93.6622859589.

It can be divided in two parts, 821 and 664, that added together give a triangular number (1485 = T₅₄).

The spelling of 821664 in words is "eight hundred twenty-one thousand, six hundred sixty-four".