513600 has 84 divisors (see below), whose sum is σ = 1700784. Its totient is φ = 135680.

The previous prime is 513593. The next prime is 513631. The reversal of 513600 is 6315.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a self number, because there is not a number n which added to its sum of digits gives 513600.

It is an unprimeable number.

513600 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 4747 + ... + 4853.

2⁵¹³⁶⁰⁰ is an apocalyptic number.

513600 is a gapful number since it is divisible by the number (50) 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 513600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (850392).

513600 is an abundant number, since it is smaller than the sum of its proper divisors (1187184).

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

513600 is a wasteful number, since it uses less digits than its factorization.

513600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 132 (or 117 counting only the distinct ones).

The product of its (nonzero) digits is 90, while the sum is 15.

The square root of 513600 is about 716.6589146868. The cubic root of 513600 is about 80.0832466782.

Adding to 513600 its reverse (6315), we get a palindrome (519915).

The spelling of 513600 in words is "five hundred thirteen thousand, six hundred".