513407541600 has 432 divisors, whose sum is σ = 1878743752704. Its totient is φ = 131787648000.

The previous prime is 513407541589. The next prime is 513407541701. The reversal of 513407541600 is 6145704315.

513407541600 is a `hidden beast` number, since 5 + 1 + 3 + 4 + 0 + 7 + 5 + 41 + 600 = 666.

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 pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 42625179 + ... + 42637221.

It is an arithmetic number, because the mean of its divisors is an integer number (4348943872).

Almost surely, 2^513407541600 is an apocalyptic number.

513407541600 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 513407541600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (939371876352).

513407541600 is an abundant number, since it is smaller than the sum of its proper divisors (1365336211104).

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

513407541600 is a wasteful number, since it uses less digits than its factorization.

513407541600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 12291 (or 12275 counting only the distinct ones).

The product of its (nonzero) digits is 50400, while the sum is 36.

The spelling of 513407541600 in words is "five hundred thirteen billion, four hundred seven million, five hundred forty-one thousand, six hundred".