814193138304 has 768 divisors, whose sum is σ = 3037961472000. Its totient is φ = 207764766720.

The previous prime is 814193138287. The next prime is 814193138309. The reversal of 814193138304 is 403831391418.

814193138304 is a `hidden beast` number, since 8 + 14 + 19 + 313 + 8 + 304 = 666.

It is a super-2 number, since 2×814193138304² (a number of 25 digits) contains 22 as substring.

It is a self number, because there is not a number n which added to its sum of digits gives 814193138304.

It is not an unprimeable number, because it can be changed into a prime (814193138309) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 159237252 + ... + 159242364.

It is an arithmetic number, because the mean of its divisors is an integer number (3955679000).

Almost surely, 2^814193138304 is an apocalyptic number.

814193138304 is a gapful number since it is divisible by the number (84) 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 814193138304, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1518980736000).

814193138304 is an abundant number, since it is smaller than the sum of its proper divisors (2223768333696).

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

814193138304 is a wasteful number, since it uses less digits than its factorization.

814193138304 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 5198 (or 5169 counting only the distinct ones).

The product of its (nonzero) digits is 248832, while the sum is 45.

The spelling of 814193138304 in words is "eight hundred fourteen billion, one hundred ninety-three million, one hundred thirty-eight thousand, three hundred four".