506464012800 has 960 divisors, whose sum is σ = 1967444075520. Its totient is φ = 127401984000.

The previous prime is 506464012793. The next prime is 506464012889. The reversal of 506464012800 is 8210464605.

506464012800 is a `hidden beast` number, since 5 + 0 + 6 + 4 + 640 + 1 + 2 + 8 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (960).

It is a super-2 number, since 2×506464012800² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

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, 439257024 + ... + 439258176.

It is an arithmetic number, because the mean of its divisors is an integer number (2049420912).

Almost surely, 2^506464012800 is an apocalyptic number.

506464012800 is a gapful number since it is divisible by the number (50) 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 506464012800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (983722037760).

506464012800 is an abundant number, since it is smaller than the sum of its proper divisors (1460980062720).

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

506464012800 is a wasteful number, since it uses less digits than its factorization.

506464012800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1262 (or 1235 counting only the distinct ones).

The product of its (nonzero) digits is 46080, while the sum is 36.

The spelling of 506464012800 in words is "five hundred six billion, four hundred sixty-four million, twelve thousand, eight hundred".