513913200 has 120 divisors (see below), whose sum is σ = 1661761200. Its totient is φ = 135751680.

The previous prime is 513913199. The next prime is 513913201. The reversal of 513913200 is 2319315.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (513913199) and next prime (513913201).

It is a tau number, because it is divible by the number of its divisors (120).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513913201) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 128836 + ... + 132764.

It is an arithmetic number, because the mean of its divisors is an integer number (13848010).

Almost surely, 2^513913200 is an apocalyptic number.

513913200 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 513913200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (830880600).

513913200 is an abundant number, since it is smaller than the sum of its proper divisors (1147848000).

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

513913200 is a wasteful number, since it uses less digits than its factorization.

513913200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 4059 (or 4048 counting only the distinct ones).

The product of its (nonzero) digits is 810, while the sum is 24.

The square root of 513913200 is about 22669.6537247484. The cubic root of 513913200 is about 800.9952197420.

The spelling of 513913200 in words is "five hundred thirteen million, nine hundred thirteen thousand, two hundred".