509961830400 has 960 divisors, whose sum is σ = 2059569072000. Its totient is φ = 122683392000.

The previous prime is 509961830383. The next prime is 509961830449. The reversal of 509961830400 is 4038169905.

It is a happy number.

509961830400 is a `hidden beast` number, since 509 + 9 + 61 + 83 + 0 + 4 + 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 2×509961830400² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3892838335 + ... + 3892838465.

It is an arithmetic number, because the mean of its divisors is an integer number (2145384450).

Almost surely, 2^509961830400 is an apocalyptic number.

509961830400 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 509961830400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1029784536000).

509961830400 is an abundant number, since it is smaller than the sum of its proper divisors (1549607241600).

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

509961830400 is an equidigital number, since it uses as much as digits as its factorization.

509961830400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 199 (or 152 counting only the distinct ones).

The product of its (nonzero) digits is 233280, while the sum is 45.

The spelling of 509961830400 in words is "five hundred nine billion, nine hundred sixty-one million, eight hundred thirty thousand, four hundred".