513374284800 has 2112 divisors, whose sum is σ = 2228812902400. Its totient is φ = 114661785600.

The previous prime is 513374284793. The next prime is 513374284823. The reversal of 513374284800 is 8482473315.

513374284800 is a `hidden beast` number, since 51 + 33 + 74 + 28 + 480 + 0 = 666.

It is a super-2 number, since 2×513374284800² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 5292518352 + ... + 5292518448.

Almost surely, 2^513374284800 is an apocalyptic number.

513374284800 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 513374284800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1114406451200).

513374284800 is an abundant number, since it is smaller than the sum of its proper divisors (1715438617600).

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

513374284800 is a wasteful number, since it uses less digits than its factorization.

513374284800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 199 (or 170 counting only the distinct ones).

The product of its (nonzero) digits is 645120, while the sum is 45.

The spelling of 513374284800 in words is "five hundred thirteen billion, three hundred seventy-four million, two hundred eighty-four thousand, eight hundred".