813424400 has 120 divisors (see below), whose sum is σ = 2009681640. Its totient is φ = 316293120.

The previous prime is 813424397. The next prime is 813424411. The reversal of 813424400 is 4424318.

It can be written as a sum of positive squares in 12 ways, for example, as 590101264 + 223323136 = 24292^2 + 14944^2 .

It is a self number, because there is not a number n which added to its sum of digits gives 813424400.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 2598644 + ... + 2598956.

It is an arithmetic number, because the mean of its divisors is an integer number (16747347).

Almost surely, 2^813424400 is an apocalyptic number.

813424400 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 813424400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1004840820).

813424400 is an abundant number, since it is smaller than the sum of its proper divisors (1196257240).

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

813424400 is a wasteful number, since it uses less digits than its factorization.

813424400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 493 (or 482 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 26.

The square root of 813424400 is about 28520.5960667024. The cubic root of 813424400 is about 933.4815354230.

Adding to 813424400 its reverse (4424318), we get a palindrome (817848718).

The spelling of 813424400 in words is "eight hundred thirteen million, four hundred twenty-four thousand, four hundred".