821000 has 32 divisors (see below), whose sum is σ = 1923480. Its totient is φ = 328000.

The previous prime is 820997. The next prime is 821003. The reversal of 821000 is 128.

It is an interprime number because it is at equal distance from previous prime (820997) and next prime (821003).

It can be written as a sum of positive squares in 4 ways, for example, as 158404 + 662596 = 398^2 + 814^2 .

It is a nialpdrome in base 10.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 821000.

It is not an unprimeable number, because it can be changed into a prime (821003) 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 7 ways as a sum of consecutive naturals, for example, 590 + ... + 1410.

2⁸²¹⁰⁰⁰ 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 821000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (961740).

821000 is an abundant number, since it is smaller than the sum of its proper divisors (1102480).

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

821000 is a wasteful number, since it uses less digits than its factorization.

821000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 842 (or 828 counting only the distinct ones).

The product of its (nonzero) digits is 16, while the sum is 11.

The square root of 821000 is about 906.0905032059. The cubic root of 821000 is about 93.6370491556.

Adding to 821000 its reverse (128), we get a palindrome (821128).

The spelling of 821000 in words is "eight hundred twenty-one thousand".