513229190400 has 648 divisors, whose sum is σ = 1893415548024. Its totient is φ = 132533452800.

The previous prime is 513229190347. The next prime is 513229190431. The reversal of 513229190400 is 4091922315.

513229190400 is a `hidden beast` number, since 5 + 13 + 229 + 19 + 0 + 400 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 756470016 + 512472720384 = 27504^2 + 715872^2 .

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 598866772 + ... + 598867628.

Almost surely, 2^513229190400 is an apocalyptic number.

513229190400 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 513229190400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (946707774012).

513229190400 is an abundant number, since it is smaller than the sum of its proper divisors (1380186357624).

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

513229190400 is a wasteful number, since it uses less digits than its factorization.

513229190400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1207 (or 1185 counting only the distinct ones).

The product of its (nonzero) digits is 19440, while the sum is 36.

The spelling of 513229190400 in words is "five hundred thirteen billion, two hundred twenty-nine million, one hundred ninety thousand, four hundred".