516412800 has 384 divisors, whose sum is σ = 1947792000. Its totient is φ = 133539840.

The previous prime is 516412777. The next prime is 516412801. The reversal of 516412800 is 8214615.

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

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (516412801) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3715131 + ... + 3715269.

It is an arithmetic number, because the mean of its divisors is an integer number (5072375).

Almost surely, 2^516412800 is an apocalyptic number.

516412800 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 516412800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (973896000).

516412800 is an abundant number, since it is smaller than the sum of its proper divisors (1431379200).

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

516412800 is a wasteful number, since it uses less digits than its factorization.

516412800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 215 (or 192 counting only the distinct ones).

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

The square root of 516412800 is about 22724.7178200302. The cubic root of 516412800 is about 802.2917618487.

The spelling of 516412800 in words is "five hundred sixteen million, four hundred twelve thousand, eight hundred".