513214120224 has 144 divisors (see below), whose sum is σ = 1576841378112. Its totient is φ = 157397313024.

The previous prime is 513214120219. The next prime is 513214120259. The reversal of 513214120224 is 422021412315.

513214120224 is a `hidden beast` number, since 5 + 1 + 3 + 21 + 412 + 0 + 224 = 666.

It is a tau number, because it is divible by the number of its divisors (144).

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 23 ways as a sum of consecutive naturals, for example, 926157 + ... + 1372659.

It is an arithmetic number, because the mean of its divisors is an integer number (10950287348).

Almost surely, 2^513214120224 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 513214120224, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (788420689056).

513214120224 is an abundant number, since it is smaller than the sum of its proper divisors (1063627257888).

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

513214120224 is a wasteful number, since it uses less digits than its factorization.

513214120224 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 446839 (or 446828 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

Adding to 513214120224 its reverse (422021412315), we get a palindrome (935235532539).

The spelling of 513214120224 in words is "five hundred thirteen billion, two hundred fourteen million, one hundred twenty thousand, two hundred twenty-four".