460816709760 has 2304 divisors, whose sum is σ = 2057039712000. Its totient is φ = 94206689280.

The previous prime is 460816709723. The next prime is 460816709791. The reversal of 460816709760 is 67907618064.

It is a happy number.

It is a junction number, because it is equal to n+sod(n) for n = 460816709697 and 460816709706.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 5177715796 + ... + 5177715884.

It is an arithmetic number, because the mean of its divisors is an integer number (892812375).

Almost surely, 2^460816709760 is an apocalyptic number.

460816709760 is a gapful number since it is divisible by the number (40) 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 460816709760, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1028519856000).

460816709760 is an abundant number, since it is smaller than the sum of its proper divisors (1596223002240).

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

460816709760 is a wasteful number, since it uses less digits than its factorization.

460816709760 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 195 (or 169 counting only the distinct ones).

The product of its (nonzero) digits is 3048192, while the sum is 54.

The spelling of 460816709760 in words is "four hundred sixty billion, eight hundred sixteen million, seven hundred nine thousand, seven hundred sixty".