513972800 has 336 divisors, whose sum is σ = 1530705600. Its totient is φ = 167731200.

The previous prime is 513972773. The next prime is 513972817. The reversal of 513972800 is 8279315.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 9697574 + ... + 9697626.

Almost surely, 2^513972800 is an apocalyptic number.

513972800 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 513972800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (765352800).

513972800 is an abundant number, since it is smaller than the sum of its proper divisors (1016732800).

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

513972800 is a wasteful number, since it uses less digits than its factorization.

513972800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 134 (or 119 counting only the distinct ones).

The product of its (nonzero) digits is 15120, while the sum is 35.

The square root of 513972800 is about 22670.9682192887. The cubic root of 513972800 is about 801.0261831224.

The spelling of 513972800 in words is "five hundred thirteen million, nine hundred seventy-two thousand, eight hundred".