513661200 has 240 divisors, whose sum is σ = 1866338880. Its totient is φ = 119715840.

The previous prime is 513661199. The next prime is 513661237. The reversal of 513661200 is 2166315.

513661200 is digitally balanced in base 6, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (24).

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, 295534 + ... + 297266.

It is an arithmetic number, because the mean of its divisors is an integer number (7776412).

Almost surely, 2^513661200 is an apocalyptic number.

513661200 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 513661200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (933169440).

513661200 is an abundant number, since it is smaller than the sum of its proper divisors (1352677680).

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

513661200 is a wasteful number, since it uses less digits than its factorization.

513661200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1786 (or 1775 counting only the distinct ones).

The product of its (nonzero) digits is 1080, while the sum is 24.

The square root of 513661200 is about 22664.0949521484. The cubic root of 513661200 is about 800.8642742845.

The spelling of 513661200 in words is "five hundred thirteen million, six hundred sixty-one thousand, two hundred".