813645000 has 600 divisors, whose sum is σ = 3393530910. Its totient is φ = 181440000.

The previous prime is 813644977. The next prime is 813645047. The reversal of 813645000 is 546318.

813645000 is a `hidden beast` number, since 8 + 13 + 645 + 0 + 0 + 0 = 666.

It can be written as a sum of positive squares in 5 ways, for example, as 24147396 + 789497604 = 4914^2 + 28098^2 .

It is a tau number, because it is divible by the number of its divisors (600).

It is a super-3 number, since 3×813645000³ (a number of 28 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 149 ways as a sum of consecutive naturals, for example, 19844980 + ... + 19845020.

Almost surely, 2^813645000 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 813645000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1696765455).

813645000 is an abundant number, since it is smaller than the sum of its proper divisors (2579885910).

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

813645000 is a wasteful number, since it uses less digits than its factorization.

813645000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 93 (or 58 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 813645000 is about 28524.4631851329. The cubic root of 813645000 is about 933.5659142597.

The spelling of 813645000 in words is "eight hundred thirteen million, six hundred forty-five thousand".