513896400 has 360 divisors, whose sum is σ = 1964499264. Its totient is φ = 128563200.

The previous prime is 513896389. The next prime is 513896423. The reversal of 513896400 is 4698315.

513896400 is a `hidden beast` number, since 5 + 1 + 3 + 8 + 9 + 640 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (360).

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, 1652245 + ... + 1652555.

Almost surely, 2^513896400 is an apocalyptic number.

513896400 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 513896400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (982249632).

513896400 is an abundant number, since it is smaller than the sum of its proper divisors (1450602864).

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

513896400 is a wasteful number, since it uses less digits than its factorization.

513896400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 361 (or 338 counting only the distinct ones).

The product of its (nonzero) digits is 25920, while the sum is 36.

The square root of 513896400 is about 22669.2831823152. The cubic root of 513896400 is about 800.9864913768.

The spelling of 513896400 in words is "five hundred thirteen million, eight hundred ninety-six thousand, four hundred".