10580 has 18 divisors (see below), whose sum is σ = 23226. Its totient is φ = 4048.

The previous prime is 10567. The next prime is 10589. The reversal of 10580 is 8501.

It can be written as a sum of positive squares in only one way, i.e., 8464 + 2116 = 92^2 + 46^2 .

It is a super-2 number, since 2×10580² = 223872800, which contains 22 as substring.

It is a nialpdrome in base 4.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (10589) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 449 + ... + 471.

2¹⁰⁵⁸⁰ is an apocalyptic number.

10580 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10580, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (11613).

10580 is an abundant number, since it is smaller than the sum of its proper divisors (12646).

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

10580 is a wasteful number, since it uses less digits than its factorization.

10580 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 55 (or 30 counting only the distinct ones).

The product of its (nonzero) digits is 40, while the sum is 14.

The square root of 10580 is about 102.8591269650. The cubic root of 10580 is about 21.9530679965.

The spelling of 10580 in words is "ten thousand, five hundred eighty".