513123072 has 144 divisors (see below), whose sum is σ = 1702831872. Its totient is φ = 133263360.

The previous prime is 513123029. The next prime is 513123073. The reversal of 513123072 is 270321315.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is not an unprimeable number, because it can be changed into a prime (513123073) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 54798 + ... + 63474.

Almost surely, 2^513123072 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 513123072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (851415936).

513123072 is an abundant number, since it is smaller than the sum of its proper divisors (1189708800).

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

513123072 is a wasteful number, since it uses less digits than its factorization.

513123072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 8714 (or 8700 counting only the distinct ones).

The product of its (nonzero) digits is 1260, while the sum is 24.

The square root of 513123072 is about 22652.2200236533. The cubic root of 513123072 is about 800.5845061700.

Adding to 513123072 its reverse (270321315), we get a palindrome (783444387).

It can be divided in two parts, 5131 and 23072, that added together give a triangular number (28203 = T₂₃₇).

The spelling of 513123072 in words is "five hundred thirteen million, one hundred twenty-three thousand, seventy-two".