513608000 has 224 divisors, whose sum is σ = 1394764800. Its totient is φ = 186624000.

The previous prime is 513607987. The next prime is 513608003. The reversal of 513608000 is 806315.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513608003) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 4711946 + ... + 4712054.

Almost surely, 2^513608000 is an apocalyptic number.

513608000 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 513608000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (697382400).

513608000 is an abundant number, since it is smaller than the sum of its proper divisors (881156800).

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

513608000 is a wasteful number, since it uses less digits than its factorization.

513608000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 186 (or 166 counting only the distinct ones).

The product of its (nonzero) digits is 720, while the sum is 23.

The square root of 513608000 is about 22662.9212591846. The cubic root of 513608000 is about 800.8366247688.

The spelling of 513608000 in words is "five hundred thirteen million, six hundred eight thousand".