513400 has 48 divisors (see below), whose sum is σ = 1272240. Its totient is φ = 192000.

The previous prime is 513397. The next prime is 513407. The reversal of 513400 is 4315.

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 11 ways as a sum of consecutive naturals, for example, 3325 + ... + 3475.

It is an arithmetic number, because the mean of its divisors is an integer number (26505).

2⁵¹³⁴⁰⁰ is an apocalyptic number.

513400 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 513400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (636120).

513400 is an abundant number, since it is smaller than the sum of its proper divisors (758840).

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

513400 is a wasteful number, since it uses less digits than its factorization.

513400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 184 (or 175 counting only the distinct ones).

The product of its (nonzero) digits is 60, while the sum is 13.

The square root of 513400 is about 716.5193647069. The cubic root of 513400 is about 80.0728503069.

Adding to 513400 its reverse (4315), we get a palindrome (517715).

The spelling of 513400 in words is "five hundred thirteen thousand, four hundred".