513872800 has 108 divisors (see below), whose sum is σ = 1459418310. Its totient is φ = 176171520.

The previous prime is 513872791. The next prime is 513872809. The reversal of 513872800 is 8278315.

It is an interprime number because it is at equal distance from previous prime (513872791) and next prime (513872809).

It can be written as a sum of positive squares in 3 ways, for example, as 352988944 + 160883856 = 18788^2 + 12684^2 .

It is not an unprimeable number, because it can be changed into a prime (513872809) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 32646 + ... + 45754.

Almost surely, 2^513872800 is an apocalyptic number.

513872800 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 513872800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (729709155).

513872800 is an abundant number, since it is smaller than the sum of its proper divisors (945545510).

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

513872800 is a wasteful number, since it uses less digits than its factorization.

513872800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 13143 (or 13123 counting only the distinct ones).

The product of its (nonzero) digits is 13440, while the sum is 34.

The square root of 513872800 is about 22668.7626481906. The cubic root of 513872800 is about 800.9742297805.

The spelling of 513872800 in words is "five hundred thirteen million, eight hundred seventy-two thousand, eight hundred".