What are the divisors of 1580?

1, 2, 4, 5, 10, 20, 79, 158, 316, 395, 790, 1580

There is a total of 12 positive divisors.
The sum of these divisors is 3360.
The arithmetic mean is 280.

8 even divisors

2, 4, 10, 20, 158, 316, 790, 1580

4 odd divisors

1, 5, 79, 395

How to compute the divisors of 1580?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 1580 by each of the numbers from 1 to 1580 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

1580 / 1 = 1580 (the remainder is 0, so 1 is a divisor of 1580)
1580 / 2 = 790 (the remainder is 0, so 2 is a divisor of 1580)
1580 / 3 = 526.66666666667 (the remainder is 2, so 3 is not a divisor of 1580)
...
1580 / 1579 = 1.0006333122229 (the remainder is 1, so 1579 is not a divisor of 1580)
1580 / 1580 = 1 (the remainder is 0, so 1580 is a divisor of 1580)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 1580 (i.e. 39.749213828704). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

1580 / 1 = 1580 (the remainder is 0, so 1 and 1580 are divisors of 1580)
1580 / 2 = 790 (the remainder is 0, so 2 and 790 are divisors of 1580)
1580 / 3 = 526.66666666667 (the remainder is 2, so 3 is not a divisor of 1580)
...
1580 / 38 = 41.578947368421 (the remainder is 22, so 38 is not a divisor of 1580)
1580 / 39 = 40.512820512821 (the remainder is 20, so 39 is not a divisor of 1580)