821312 has 28 divisors (see below), whose sum is σ = 1674876. Its totient is φ = 399360.

The previous prime is 821311. The next prime is 821329. The reversal of 821312 is 213128.

It can be written as a sum of positive squares in 2 ways, for example, as 18496 + 802816 = 136^2 + 896^2 .

It is a plaindrome in base 13.

It is a nialpdrome in base 16.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (821311) 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, 2468 + ... + 2780.

It is an arithmetic number, because the mean of its divisors is an integer number (59817).

2⁸²¹³¹² is an apocalyptic number.

821312 is a gapful number since it is divisible by the number (82) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 821312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (837438).

821312 is an abundant number, since it is smaller than the sum of its proper divisors (853564).

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

821312 is a wasteful number, since it uses less digits than its factorization.

821312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 366 (or 356 counting only the distinct ones).

The product of its digits is 96, while the sum is 17.

The square root of 821312 is about 906.2626550841. The cubic root of 821312 is about 93.6489091067.

It can be divided in two parts, 82 and 1312, that multiplied together give a square (107584 = 328²).

The spelling of 821312 in words is "eight hundred twenty-one thousand, three hundred twelve".