513304000 has 224 divisors, whose sum is σ = 1464503040. Its totient is φ = 176256000.

The previous prime is 513303971. The next prime is 513304003. The reversal of 513304000 is 403315.

It is a Harshad number since it is a multiple of its sum of digits (16).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513304003) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 1671847 + ... + 1672153.

It is an arithmetic number, because the mean of its divisors is an integer number (6537960).

Almost surely, 2^513304000 is an apocalyptic number.

513304000 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 513304000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (732251520).

513304000 is an abundant number, since it is smaller than the sum of its proper divisors (951199040).

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

513304000 is a wasteful number, since it uses less digits than its factorization.

513304000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 364 (or 344 counting only the distinct ones).

The product of its (nonzero) digits is 180, while the sum is 16.

The square root of 513304000 is about 22656.2132758323. The cubic root of 513304000 is about 800.6785908969.

Adding to 513304000 its reverse (403315), we get a palindrome (513707315).

The spelling of 513304000 in words is "five hundred thirteen million, three hundred four thousand".