463105513728 has 864 divisors, whose sum is σ = 1689158983680. Its totient is φ = 123828756480.

The previous prime is 463105513727. The next prime is 463105513747. The reversal of 463105513728 is 827315501364.

It is a happy number.

463105513728 is a `hidden beast` number, since 4 + 6 + 3 + 105 + 513 + 7 + 28 = 666.

It is a tau number, because it is divible by the number of its divisors (864).

It is not an unprimeable number, because it can be changed into a prime (463105513727) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 295535601 + ... + 295537167.

It is an arithmetic number, because the mean of its divisors is an integer number (1955045120).

Almost surely, 2^463105513728 is an apocalyptic number.

463105513728 is a gapful number since it is divisible by the number (48) 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 463105513728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (844579491840).

463105513728 is an abundant number, since it is smaller than the sum of its proper divisors (1226053469952).

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

463105513728 is a wasteful number, since it uses less digits than its factorization.

463105513728 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1652 (or 1619 counting only the distinct ones).

The product of its (nonzero) digits is 604800, while the sum is 45.

The spelling of 463105513728 in words is "four hundred sixty-three billion, one hundred five million, five hundred thirteen thousand, seven hundred twenty-eight".