513838224 has 45 divisors (see below), whose sum is σ = 1438795033. Its totient is φ = 171188736.

The previous prime is 513838201. The next prime is 513838249. The reversal of 513838224 is 422838315.

The square root of 513838224 is 22668.

It is a perfect power (a square), and thus also a powerful number.

513838224 is a `hidden beast` number, since 51 + 383 + 8 + 224 = 666.

It can be written as a sum of positive squares in only one way, i.e., 247495824 + 266342400 = 15732^2 + 16320^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a Duffinian number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 271072 + ... + 272960.

Almost surely, 2^513838224 is an apocalyptic number.

513838224 is the 22668-th square number.

It is an amenable number.

513838224 is an abundant number, since it is smaller than the sum of its proper divisors (924956809).

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

513838224 is an equidigital number, since it uses as much as digits as its factorization.

513838224 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3792 (or 1894 counting only the distinct ones).

The product of its digits is 46080, while the sum is 36.

The cubic root of 513838224 is about 800.9562648249.

Multiplying 513838224 by its sum of digits (36), we get a square (18498176064 = 136008²).

513838224 divided by its sum of digits (36) gives a square (14273284 = 3778²).

Subtracting from 513838224 its reverse (422838315), we obtain a palindrome (90999909).

The spelling of 513838224 in words is "five hundred thirteen million, eight hundred thirty-eight thousand, two hundred twenty-four".