513382320 has 640 divisors, whose sum is σ = 2159861760. Its totient is φ = 110592000.

The previous prime is 513382313. The next prime is 513382357. The reversal of 513382320 is 23283315.

513382320 = T₁₈₅ + T₁₈₆ + ... + T₁₄₅₅.

513382320 is a `hidden beast` number, since 5 + 1 + 338 + 2 + 320 = 666.

It is a super-2 number, since 2×513382320² = 527122812977164800, which contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 12521500 + ... + 12521540.

It is an arithmetic number, because the mean of its divisors is an integer number (3374784).

Almost surely, 2^513382320 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 513382320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1079930880).

513382320 is an abundant number, since it is smaller than the sum of its proper divisors (1646479440).

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

513382320 is a wasteful number, since it uses less digits than its factorization.

513382320 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 122 (or 110 counting only the distinct ones).

The product of its (nonzero) digits is 4320, while the sum is 27.

The square root of 513382320 is about 22657.9416540868. The cubic root of 513382320 is about 800.7193113784.

The spelling of 513382320 in words is "five hundred thirteen million, three hundred eighty-two thousand, three hundred twenty".