513516960 has 288 divisors, whose sum is σ = 2025196992. Its totient is φ = 117104640.

The previous prime is 513516937. The next prime is 513516961. The reversal of 513516960 is 69615315.

513516960 is a `hidden beast` number, since 51 + 3 + 516 + 96 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513516961) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 268327 + ... + 270233.

It is an arithmetic number, because the mean of its divisors is an integer number (7031934).

Almost surely, 2^513516960 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 513516960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1012598496).

513516960 is an abundant number, since it is smaller than the sum of its proper divisors (1511680032).

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

513516960 is a wasteful number, since it uses less digits than its factorization.

513516960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1956 (or 1945 counting only the distinct ones).

The product of its (nonzero) digits is 24300, while the sum is 36.

The square root of 513516960 is about 22660.9126029823. The cubic root of 513516960 is about 800.7893043256.

It can be divided in two parts, 51351 and 6960, that added together give a triangular number (58311 = T₃₄₁).

The spelling of 513516960 in words is "five hundred thirteen million, five hundred sixteen thousand, nine hundred sixty".