513624672 has 288 divisors, whose sum is σ = 1749535200. Its totient is φ = 146488320.

The previous prime is 513624649. The next prime is 513624679. The reversal of 513624672 is 276426315.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a tau number, because it is divible by the number of its divisors (288).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513624679) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 30213208 + ... + 30213224.

It is an arithmetic number, because the mean of its divisors is an integer number (6074775).

Almost surely, 2^513624672 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 513624672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (874767600).

513624672 is an abundant number, since it is smaller than the sum of its proper divisors (1235910528).

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

513624672 is a wasteful number, since it uses less digits than its factorization.

513624672 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 92 (or 33 counting only the distinct ones).

The product of its digits is 60480, while the sum is 36.

The square root of 513624672 is about 22663.2890816845. The cubic root of 513624672 is about 800.8452898750.

The spelling of 513624672 in words is "five hundred thirteen million, six hundred twenty-four thousand, six hundred seventy-two".