513408000 has 352 divisors, whose sum is σ = 1961975808. Its totient is φ = 116736000.

The previous prime is 513407977. The next prime is 513408011. The reversal of 513408000 is 804315.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 2687905 + ... + 2688095.

Almost surely, 2^513408000 is an apocalyptic number.

513408000 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 513408000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (980987904).

513408000 is an abundant number, since it is smaller than the sum of its proper divisors (1448567808).

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

513408000 is a wasteful number, since it uses less digits than its factorization.

513408000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 236 (or 208 counting only the distinct ones).

The product of its (nonzero) digits is 480, while the sum is 21.

The square root of 513408000 is about 22658.5083357224. The cubic root of 513408000 is about 800.7326621362.

It can be divided in two parts, 51340 and 8000, that added together give a triangular number (59340 = T₃₄₄).

The spelling of 513408000 in words is "five hundred thirteen million, four hundred eight thousand".