820478880 has 288 divisors, whose sum is σ = 3091692240. Its totient is φ = 196853760.

The previous prime is 820478831. The next prime is 820478887. The reversal of 820478880 is 88874028.

It can be written as a sum of positive squares in 8 ways, for example, as 39388176 + 781090704 = 6276^2 + 27948^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (820478887) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 766986 + ... + 768054.

Almost surely, 2^820478880 is an apocalyptic number.

820478880 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 820478880, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1545846120).

820478880 is an abundant number, since it is smaller than the sum of its proper divisors (2271213360).

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

820478880 is a wasteful number, since it uses less digits than its factorization.

820478880 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1144 (or 1133 counting only the distinct ones).

The product of its (nonzero) digits is 229376, while the sum is 45.

The square root of 820478880 is about 28644.0025136153. The cubic root of 820478880 is about 936.1723329411.

The spelling of 820478880 in words is "eight hundred twenty million, four hundred seventy-eight thousand, eight hundred eighty".