513264 has 60 divisors (see below), whose sum is σ = 1446584. Its totient is φ = 156672.

The previous prime is 513257. The next prime is 513269. The reversal of 513264 is 462315.

It is a happy number.

It is a self number, because there is not a number n which added to its sum of digits gives 513264.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513269) by changing a digit.

513264 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 11 ways as a sum of consecutive naturals, for example, 13854 + ... + 13890.

2⁵¹³²⁶⁴ 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 513264, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (723292).

513264 is an abundant number, since it is smaller than the sum of its proper divisors (933320).

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

513264 is a wasteful number, since it uses less digits than its factorization.

513264 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 82 (or 59 counting only the distinct ones).

The product of its digits is 720, while the sum is 21.

The square root of 513264 is about 716.4244551940. The cubic root of 513264 is about 80.0657792322.

Adding to 513264 its reverse (462315), we get a palindrome (975579).

It can be divided in two parts, 513 and 264, that added together give a palindrome (777).

The spelling of 513264 in words is "five hundred thirteen thousand, two hundred sixty-four".