513424800 has 432 divisors, whose sum is σ = 2115614592. Its totient is φ = 114739200.

The previous prime is 513424799. The next prime is 513424801. The reversal of 513424800 is 8424315.

It is an interprime number because it is at equal distance from previous prime (513424799) and next prime (513424801).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513424801) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 3074317 + ... + 3074483.

It is an arithmetic number, because the mean of its divisors is an integer number (4897256).

Almost surely, 2^513424800 is an apocalyptic number.

513424800 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 513424800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1057807296).

513424800 is an abundant number, since it is smaller than the sum of its proper divisors (1602189792).

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

513424800 is a wasteful number, since it uses less digits than its factorization.

513424800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 261 (or 245 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

The square root of 513424800 is about 22658.8790543575. The cubic root of 513424800 is about 800.7413960360.

The spelling of 513424800 in words is "five hundred thirteen million, four hundred twenty-four thousand, eight hundred".