513315000 has 480 divisors, whose sum is σ = 2039534640. Its totient is φ = 115200000.

The previous prime is 513314981. The next prime is 513315007. The reversal of 513315000 is 513315.

It is a happy number.

513315000 is a `hidden beast` number, since 513 + 3 + 150 + 0 + 0 = 666.

It is a super-3 number, since 3×513315000³ (a number of 27 digits) contains 333 as substring.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513315007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 8414970 + ... + 8415030.

Almost surely, 2^513315000 is an apocalyptic number.

513315000 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 513315000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1019767320).

513315000 is an abundant number, since it is smaller than the sum of its proper divisors (1526219640).

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

513315000 is a wasteful number, since it uses less digits than its factorization.

513315000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 121 (or 99 counting only the distinct ones).

The product of its (nonzero) digits is 225, while the sum is 18.

The square root of 513315000 is about 22656.4560335459. The cubic root of 513315000 is about 800.6843103157.

Adding to 513315000 its reverse (513315), we get a palindrome (513828315).

513315000 divided by its reverse (513315) gives a cube (1000 = 10³).

It can be divided in two parts, 513 and 315000, that added together give a palindrome (315513).

The spelling of 513315000 in words is "five hundred thirteen million, three hundred fifteen thousand".