513378000 has 200 divisors, whose sum is σ = 1854944520. Its totient is φ = 136857600.

The previous prime is 513377993. The next prime is 513378001. The reversal of 513378000 is 873315.

It can be written as a sum of positive squares in 4 ways, for example, as 627264 + 512750736 = 792^2 + 22644^2 .

It is a tau number, because it is divible by the number of its divisors (200).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513378001) by changing a digit.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 160416 + ... + 163584.

Almost surely, 2^513378000 is an apocalyptic number.

513378000 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 513378000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (927472260).

513378000 is an abundant number, since it is smaller than the sum of its proper divisors (1341566520).

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

513378000 is a wasteful number, since it uses less digits than its factorization.

513378000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3204 (or 3179 counting only the distinct ones).

The product of its (nonzero) digits is 2520, while the sum is 27.

The square root of 513378000 is about 22657.8463230732. The cubic root of 513378000 is about 800.7170654128.

The spelling of 513378000 in words is "five hundred thirteen million, three hundred seventy-eight thousand".