506407744972800 has 1728 divisors, whose sum is σ = 2117978620692480. Its totient is φ = 118804340736000.

The previous prime is 506407744972783. The next prime is 506407744972847. The reversal of 506407744972800 is 8279447704605.

506407744972800 is a `hidden beast` number, since 5 + 0 + 6 + 40 + 7 + 7 + 449 + 72 + 80 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1728).

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 4242525919 + ... + 4242645281.

It is an arithmetic number, because the mean of its divisors is an integer number (1225682072160).

Almost surely, 2^{506407744972800} is an apocalyptic number.

506407744972800 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 506407744972800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1058989310346240).

506407744972800 is an abundant number, since it is smaller than the sum of its proper divisors (1611570875719680).

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

506407744972800 is a wasteful number, since it uses less digits than its factorization.

506407744972800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 119452 (or 119415 counting only the distinct ones).

The product of its (nonzero) digits is 94832640, while the sum is 63.

The spelling of 506407744972800 in words is "five hundred six trillion, four hundred seven billion, seven hundred forty-four million, nine hundred seventy-two thousand, eight hundred".