513820800 has 384 divisors, whose sum is σ = 1985736000. Its totient is φ = 129392640.

The previous prime is 513820777. The next prime is 513820847. The reversal of 513820800 is 8028315.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (384).

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1641444 + ... + 1641756.

Almost surely, 2^513820800 is an apocalyptic number.

513820800 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 513820800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (992868000).

513820800 is an abundant number, since it is smaller than the sum of its proper divisors (1471915200).

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

513820800 is a wasteful number, since it uses less digits than its factorization.

513820800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 365 (or 342 counting only the distinct ones).

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

The square root of 513820800 is about 22667.6156664083. The cubic root of 513820800 is about 800.9472113790.

It can be divided in two parts, 513 and 820800, that multiplied together give a square (421070400 = 20520²).

The spelling of 513820800 in words is "five hundred thirteen million, eight hundred twenty thousand, eight hundred".