820727028 has 216 divisors, whose sum is σ = 2418179400. Its totient is φ = 234178560.

The previous prime is 820727027. The next prime is 820727041.

820727028 is nontrivially palindromic in base 10.

It can be written as a sum of positive squares in 4 ways, for example, as 59629284 + 761097744 = 7722^2 + 27588^2 .

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

It is a junction number, because it is equal to n+sod(n) for n = 820726983 and 820727001.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (820727027) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 9221608 + ... + 9221696.

It is an arithmetic number, because the mean of its divisors is an integer number (11195275).

Almost surely, 2^820727028 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 820727028, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1209089700).

820727028 is an abundant number, since it is smaller than the sum of its proper divisors (1597452372).

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

820727028 is a wasteful number, since it uses less digits than its factorization.

820727028 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 223 (or 207 counting only the distinct ones).

The product of its (nonzero) digits is 25088, while the sum is 36.

The square root of 820727028 is about 28648.3337735373. Note that the first 3 decimals coincide. The cubic root of 820727028 is about 936.2667029818.

The spelling of 820727028 in words is "eight hundred twenty million, seven hundred twenty-seven thousand, twenty-eight".