513963072 has 168 divisors, whose sum is σ = 1772513600. Its totient is φ = 139097088.

The previous prime is 513963049. The next prime is 513963077. The reversal of 513963072 is 270369315.

513963072 is a `hidden beast` number, since 5 + 13 + 9 + 630 + 7 + 2 = 666.

It is a tau number, because it is divible by the number of its divisors (168).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (513963077) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 73254 + ... + 79962.

Almost surely, 2^513963072 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 513963072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (886256800).

513963072 is an abundant number, since it is smaller than the sum of its proper divisors (1258550528).

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

513963072 is a wasteful number, since it uses less digits than its factorization.

513963072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 6753 (or 6740 counting only the distinct ones).

The product of its (nonzero) digits is 34020, while the sum is 36.

The square root of 513963072 is about 22670.7536707539. The cubic root of 513963072 is about 801.0211293972.

The spelling of 513963072 in words is "five hundred thirteen million, nine hundred sixty-three thousand, seventy-two".