513240219648000 has 2880 divisors, whose sum is σ = 2094874722420480. Its totient is φ = 124259401728000.

The previous prime is 513240219647989. The next prime is 513240219648029. The reversal of 513240219648000 is 846912042315.

513240219648000 is a `hidden beast` number, since 5 + 13 + 2 + 402 + 196 + 48 + 0 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2880).

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 159 ways as a sum of consecutive naturals, for example, 1224916991791 + ... + 1224916992209.

It is an arithmetic number, because the mean of its divisors is an integer number (727387056396).

Almost surely, 2^{513240219648000} is an apocalyptic number.

513240219648000 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 513240219648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1047437361210240).

513240219648000 is an abundant number, since it is smaller than the sum of its proper divisors (1581634502772480).

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

513240219648000 is an frugal number, since it uses more digits than its factorization.

513240219648000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 564 (or 513 counting only the distinct ones).

The product of its (nonzero) digits is 414720, while the sum is 45.

The spelling of 513240219648000 in words is "five hundred thirteen trillion, two hundred forty billion, two hundred nineteen million, six hundred forty-eight thousand".