513324 has 72 divisors (see below), whose sum is σ = 1564080. Its totient is φ = 145152.

The previous prime is 513319. The next prime is 513341. The reversal of 513324 is 423315.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 14.

It is a junction number, because it is equal to n+sod(n) for n = 513297 and 513306.

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 513324.

It is an unprimeable number.

513324 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 23 ways as a sum of consecutive naturals, for example, 5244 + ... + 5340.

2⁵¹³³²⁴ is an apocalyptic number.

513324 is a gapful number since it is divisible by the number (54) 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 513324, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (782040).

513324 is an abundant number, since it is smaller than the sum of its proper divisors (1050756).

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

513324 is a wasteful number, since it uses less digits than its factorization.

513324 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 124 (or 109 counting only the distinct ones).

The product of its digits is 360, while the sum is 18.

The square root of 513324 is about 716.4663285877. The cubic root of 513324 is about 80.0688989779.

Adding to 513324 its reverse (423315), we get a palindrome (936639).

Subtracting from 513324 its reverse (423315), we obtain a palindrome (90009).

It can be divided in two parts, 51 and 3324, that added together give a cube (3375 = 15³).

The spelling of 513324 in words is "five hundred thirteen thousand, three hundred twenty-four".