513216000 has 560 divisors, whose sum is σ = 2093156208. Its totient is φ = 124416000.

The previous prime is 513215993. The next prime is 513216019. The reversal of 513216000 is 612315.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 55 ways as a sum of consecutive naturals, for example, 46655995 + ... + 46656005.

Almost surely, 2^513216000 is an apocalyptic number.

513216000 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 513216000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1046578104).

513216000 is an abundant number, since it is smaller than the sum of its proper divisors (1579940208).

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

513216000 is an frugal number, since it uses more digits than its factorization.

513216000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 62 (or 21 counting only the distinct ones).

The product of its (nonzero) digits is 180, while the sum is 18.

The square root of 513216000 is about 22654.2711204753. The cubic root of 513216000 is about 800.6328326050.

Adding to 513216000 its reverse (612315), we get a palindrome (513828315).

The spelling of 513216000 in words is "five hundred thirteen million, two hundred sixteen thousand".