820509872400 has 405 divisors, whose sum is σ = 2948265558693. Its totient is φ = 211309689600.

The previous prime is 820509872359. The next prime is 820509872407. The reversal of 820509872400 is 4278905028.

The square root of 820509872400 is 905820.

It is a perfect power (a square), and thus also a powerful number.

820509872400 is a `hidden beast` number, since 8 + 20 + 509 + 87 + 2 + 40 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 295383554064 + 525126318336 = 543492^2 + 724656^2 .

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 (820509872407) by changing a digit.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 1684824957 + ... + 1684825443.

Almost surely, 2^820509872400 is an apocalyptic number.

820509872400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

820509872400 is the 905820-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 820509872400

820509872400 is an abundant number, since it is smaller than the sum of its proper divisors (2127755686293).

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

820509872400 is a wasteful number, since it uses less digits than its factorization.

820509872400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1060 (or 528 counting only the distinct ones).

The product of its (nonzero) digits is 322560, while the sum is 45.

The spelling of 820509872400 in words is "eight hundred twenty billion, five hundred nine million, eight hundred seventy-two thousand, four hundred".