512000 has 52 divisors (see below), whose sum is σ = 1277796. Its totient is φ = 204800.

The previous prime is 511997. The next prime is 512009. The reversal of 512000 is 215.

The cubic root of 512000 is 80.

It is a perfect power (a cube), and thus also a powerful number.

It can be written as a sum of positive squares in 2 ways, for example, as 16384 + 495616 = 128^2 + 704^2 .

It is a Harshad number since it is a multiple of its sum of digits (8).

It is a zygodrome in base 3.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (512009) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 102398 + ... + 102402.

It is an arithmetic number, because the mean of its divisors is an integer number (24573).

512000 is a Friedman number, since it can be written as 500*2^10, using all its digits and the basic arithmetic operations.

2⁵¹²⁰⁰⁰ is an apocalyptic number.

512000 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 512000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (638898).

512000 is an abundant number, since it is smaller than the sum of its proper divisors (765796).

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

512000 is an frugal number, since it uses more digits than its factorization.

512000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 39 (or 7 counting only the distinct ones).

The product of its (nonzero) digits is 10, while the sum is 8.

The square root of 512000 is about 715.5417527999.

Adding to 512000 its reverse (215), we get a palindrome (512215).

The spelling of 512000 in words is "five hundred twelve thousand".