513928800 has 720 divisors, whose sum is σ = 2359348992. Its totient is φ = 105753600.

The previous prime is 513928783. The next prime is 513928823. The reversal of 513928800 is 8829315.

It is a tau number, because it is divible by the number of its divisors (720).

It is a super-2 number, since 2×513928800² = 528245622938880000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 4989549 + ... + 4989651.

Almost surely, 2^513928800 is an apocalyptic number.

513928800 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 513928800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1179674496).

513928800 is an abundant number, since it is smaller than the sum of its proper divisors (1845420192).

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

513928800 is a wasteful number, since it uses less digits than its factorization.

513928800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 153 (or 131 counting only the distinct ones).

The product of its (nonzero) digits is 17280, while the sum is 36.

The square root of 513928800 is about 22669.9977944419. The cubic root of 513928800 is about 801.0033244823.

The spelling of 513928800 in words is "five hundred thirteen million, nine hundred twenty-eight thousand, eight hundred".