513638400 has 384 divisors, whose sum is σ = 1950321600. Its totient is φ = 117964800.

The previous prime is 513638399. The next prime is 513638407. The reversal of 513638400 is 4836315.

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513638407) 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, 27033591 + ... + 27033609.

Almost surely, 2^513638400 is an apocalyptic number.

513638400 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 513638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (975160800).

513638400 is an abundant number, since it is smaller than the sum of its proper divisors (1436683200).

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

513638400 is a wasteful number, since it uses less digits than its factorization.

513638400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 73 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 8640, while the sum is 30.

The square root of 513638400 is about 22663.5919483210. The cubic root of 513638400 is about 800.8524247258.

The spelling of 513638400 in words is "five hundred thirteen million, six hundred thirty-eight thousand, four hundred".