513028800 has 252 divisors, whose sum is σ = 1903933200. Its totient is φ = 130775040.

The previous prime is 513028783. The next prime is 513028801. The reversal of 513028800 is 8820315.

It is a happy number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513028801) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 330426 + ... + 331974.

Almost surely, 2^513028800 is an apocalyptic number.

513028800 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 513028800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (951966600).

513028800 is an abundant number, since it is smaller than the sum of its proper divisors (1390904400).

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

513028800 is a wasteful number, since it uses less digits than its factorization.

513028800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1600 (or 1582 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 27.

The square root of 513028800 is about 22650.1390724207. The cubic root of 513028800 is about 800.5354748367.

It can be divided in two parts, 5130 and 28800, that added together give a triangular number (33930 = T₂₆₀).

The spelling of 513028800 in words is "five hundred thirteen million, twenty-eight thousand, eight hundred".