517968 has 80 divisors (see below), whose sum is σ = 1636800. Its totient is φ = 155520.

The previous prime is 517967. The next prime is 517981. The reversal of 517968 is 869715.

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

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 517968.

It is not an unprimeable number, because it can be changed into a prime (517967) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 4698 + ... + 4806.

It is an arithmetic number, because the mean of its divisors is an integer number (20460).

2⁵¹⁷⁹⁶⁸ 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 517968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (818400).

517968 is an abundant number, since it is smaller than the sum of its proper divisors (1118832).

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

517968 is a wasteful number, since it uses less digits than its factorization.

517968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 137 (or 125 counting only the distinct ones).

The product of its digits is 15120, while the sum is 36.

The square root of 517968 is about 719.6999374739. The cubic root of 517968 is about 80.3096333769.

It can be divided in two parts, 517 and 968, that added together give a triangular number (1485 = T₅₄).

The spelling of 517968 in words is "five hundred seventeen thousand, nine hundred sixty-eight".