820872 has 48 divisors (see below), whose sum is σ = 2396940. Its totient is φ = 252288.

The previous prime is 820837. The next prime is 820873. The reversal of 820872 is 278028.

It can be written as a sum of positive squares in 2 ways, for example, as 820836 + 36 = 906^2 + 6^2 .

It is a plaindrome in base 15.

It is not an unprimeable number, because it can be changed into a prime (820873) by changing a digit.

820872 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 11 ways as a sum of consecutive naturals, for example, 498 + ... + 1374.

2⁸²⁰⁸⁷² 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 820872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1198470).

820872 is an abundant number, since it is smaller than the sum of its proper divisors (1576068).

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

820872 is a wasteful number, since it uses less digits than its factorization.

820872 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 902 (or 895 counting only the distinct ones).

The product of its (nonzero) digits is 1792, while the sum is 27.

The square root of 820872 is about 906.0198673318. The cubic root of 820872 is about 93.6321826655.

The spelling of 820872 in words is "eight hundred twenty thousand, eight hundred seventy-two".