820306872 has 512 divisors, whose sum is σ = 3081830400. Its totient is φ = 195955200.

The previous prime is 820306871. The next prime is 820306901. The reversal of 820306872 is 278603028.

It is a happy number.

820306872 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a super-3 number, since 3×820306872³ (a number of 28 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (820306871) by changing a digit.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 19076883 + ... + 19076925.

It is an arithmetic number, because the mean of its divisors is an integer number (6019200).

Almost surely, 2^820306872 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 820306872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1540915200).

820306872 is an abundant number, since it is smaller than the sum of its proper divisors (2261523528).

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

820306872 is a wasteful number, since it uses less digits than its factorization.

820306872 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 144 (or 134 counting only the distinct ones).

The product of its (nonzero) digits is 32256, while the sum is 36.

The square root of 820306872 is about 28640.9998428826. Note that the first 3 decimals coincide. The cubic root of 820306872 is about 936.1069075784.

The spelling of 820306872 in words is "eight hundred twenty million, three hundred six thousand, eight hundred seventy-two".