What are the divisors of 260?

1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260

There is a total of 12 positive divisors.
The sum of these divisors is 588.
The arithmetic mean is 49.

8 even divisors

2, 4, 10, 20, 26, 52, 130, 260

4 odd divisors

1, 5, 13, 65

How to compute the divisors of 260?

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 260 by each of the numbers from 1 to 260 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)

260 / 1 = 260 (the remainder is 0, so 1 is a divisor of 260)
260 / 2 = 130 (the remainder is 0, so 2 is a divisor of 260)
260 / 3 = 86.666666666667 (the remainder is 2, so 3 is not a divisor of 260)
...
260 / 259 = 1.003861003861 (the remainder is 1, so 259 is not a divisor of 260)
260 / 260 = 1 (the remainder is 0, so 260 is a divisor of 260)

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 260 (i.e. 16.124515496597). 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 $\frac{N}{d} = D$ )

260 / 1 = 260 (the remainder is 0, so 1 and 260 are divisors of 260)
260 / 2 = 130 (the remainder is 0, so 2 and 130 are divisors of 260)
260 / 3 = 86.666666666667 (the remainder is 2, so 3 is not a divisor of 260)
...
260 / 15 = 17.333333333333 (the remainder is 5, so 15 is not a divisor of 260)
260 / 16 = 16.25 (the remainder is 4, so 16 is not a divisor of 260)