509973871680 has 1344 divisors, whose sum is σ = 2365305546240. Its totient is φ = 97752711168.

The previous prime is 509973871609. The next prime is 509973871703. The reversal of 509973871680 is 86178379905.

509973871680 is a `hidden beast` number, since 5 + 0 + 9 + 97 + 387 + 168 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1344).

It is a hoax number, since the sum of its digits (63) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (63).

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 129203467 + ... + 129207413.

It is an arithmetic number, because the mean of its divisors is an integer number (1759899960).

Almost surely, 2^509973871680 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 509973871680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1182652773120).

509973871680 is an abundant number, since it is smaller than the sum of its proper divisors (1855331674560).

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

509973871680 is a wasteful number, since it uses less digits than its factorization.

509973871680 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 4036 (or 4023 counting only the distinct ones).

The product of its (nonzero) digits is 22861440, while the sum is 63.

The spelling of 509973871680 in words is "five hundred nine billion, nine hundred seventy-three million, eight hundred seventy-one thousand, six hundred eighty".