513408 has 64 divisors (see below), whose sum is σ = 1566720. Its totient is φ = 145920.

The previous prime is 513407. The next prime is 513419. The reversal of 513408 is 804315.

It is a tau number, because it is divible by the number of its divisors (64).

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513407) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 2593 + ... + 2783.

It is an arithmetic number, because the mean of its divisors is an integer number (24480).

2⁵¹³⁴⁰⁸ 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 513408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (783360).

513408 is an abundant number, since it is smaller than the sum of its proper divisors (1053312).

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

513408 is a wasteful number, since it uses less digits than its factorization.

513408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 215 (or 203 counting only the distinct ones).

The product of its (nonzero) digits is 480, while the sum is 21.

The square root of 513408 is about 716.5249472279. The cubic root of 513408 is about 80.0732662136.

The spelling of 513408 in words is "five hundred thirteen thousand, four hundred eight".