820 has 12 divisors (see below), whose sum is σ = 1764. Its totient is φ = 320.

The previous prime is 811. The next prime is 821. The reversal of 820 is 28.

It is a happy number.

820 is nontrivially palindromic in base 3, base 9 and base 11.

820 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

820 is an esthetic number in base 3, because in such base its adjacent digits differ by 1.

820 is a nontrivial binomial coefficient, being equal to C(41, 2).

It can be written as a sum of positive squares in 2 ways, for example, as 144 + 676 = 12^2 + 26^2 .

It is a Harshad number since it is a multiple of its sum of digits (10).

It is an Ulam number.

820 is an undulating number in base 3 and base 11.

820 is a nontrivial repdigit in base 9.

It is a plaindrome in base 6, base 9, base 15 and base 16.

It is a nialpdrome in base 9 and base 10.

It is a zygodrome in base 9.

It is a junction number, because it is equal to n+sod(n) for n = 797 and 806.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (821) by changing a digit.

It is a nontrivial repunit in base 9.

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, 1 + ... + 40.

It is an arithmetic number, because the mean of its divisors is an integer number (147).

2⁸²⁰ is an apocalyptic number.

820 is the 40-th triangular number.

820 is the 14-th centered nonagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 820, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (882).

820 is an abundant number, since it is smaller than the sum of its proper divisors (944).

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

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

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

The sum of its prime factors is 50 (or 48 counting only the distinct ones).

The product of its (nonzero) digits is 16, while the sum is 10.

The square root of 820 is about 28.6356421266. The cubic root of 820 is about 9.3599016231.

Adding to 820 its reverse (28), we get a palindrome (848).

It can be divided in two parts, 8 and 20, that added together give a triangular number (28 = T₇).

The spelling of 820 in words is "eight hundred twenty", and thus it is an aban number and an oban number.