58320 has 70 divisors (see below), whose sum is σ = 203298. Its totient is φ = 15552.

The previous prime is 58313. The next prime is 58321. The reversal of 58320 is 2385.

58320 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in only one way, i.e., 46656 + 11664 = 216^2 + 108^2 .

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

It is a nialpdrome in base 3 and base 9.

It is a zygodrome in base 3 and base 9.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 58293 and 58302.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (58321) by changing a digit.

58320 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 13 ways as a sum of consecutive naturals, for example, 11662 + ... + 11666.

2^{58320} 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 58320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (101649).

58320 is an abundant number, since it is smaller than the sum of its proper divisors (144978).

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

58320 is an equidigital number, since it uses as much as digits as its factorization.

58320 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 31 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 240, while the sum is 18.

The square root of 58320 is about 241.4953415700. The cubic root of 58320 is about 38.7798244206.

58320 divided by its sum of digits (18) gives a triangular number (3240 = T_{80}).

58320 divided by its product of nonzero digits (240) gives a 5-th power (243 = 3^{5}).

It can be divided in two parts, 58 and 320, that added together give a triangular number (378 = T_{27}).

The spelling of 58320 in words is "fifty-eight thousand, three hundred twenty".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 36 40 45 48 54 60 72 80 81 90 108 120 135 144 162 180 216 240 243 270 324 360 405 432 486 540 648 720 729 810 972 1080 1215 1296 1458 1620 1944 2160 2430 2916 3240 3645 3888 4860 5832 6480 7290 9720 11664 14580 19440 29160 58320

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