1580 has 12 divisors (see below), whose sum is σ = 3360. Its totient is φ = 624.

The previous prime is 1579. The next prime is 1583. The reversal of 1580 is 851.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1583) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 20 + ... + 59.

It is an arithmetic number, because the mean of its divisors is an integer number (280).

1580 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

1580 is an abundant number, since it is smaller than the sum of its proper divisors (1780).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1680).

1580 is a wasteful number, since it uses less digits than its factorization.

1580 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 88 (or 86 counting only the distinct ones).

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

The square root of 1580 is about 39.7492138287. The cubic root of 1580 is about 11.6471328451.

Subtracting from 1580 its product of nonzero digits (40), we obtain a triangular number (1540 = T₅₅).

Subtracting from 1580 its reverse (851), we obtain a 6-th power (729 = 3⁶).

The spelling of 1580 in words is "one thousand, five hundred eighty".