What are the divisors of 5260?

1, 2, 4, 5, 10, 20, 263, 526, 1052, 1315, 2630, 5260

There is a total of 12 positive divisors.
The sum of these divisors is 11088.
The arithmetic mean is 924.

8 even divisors

2, 4, 10, 20, 526, 1052, 2630, 5260

4 odd divisors

1, 5, 263, 1315

How to compute the divisors of 5260?

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 5260 by each of the numbers from 1 to 5260 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)

5260 / 1 = 5260 (the remainder is 0, so 1 is a divisor of 5260)
5260 / 2 = 2630 (the remainder is 0, so 2 is a divisor of 5260)
5260 / 3 = 1753.3333333333 (the remainder is 1, so 3 is not a divisor of 5260)
...
5260 / 5259 = 1.0001901502187 (the remainder is 1, so 5259 is not a divisor of 5260)
5260 / 5260 = 1 (the remainder is 0, so 5260 is a divisor of 5260)

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 5260 (i.e. 72.525857457875). 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 $\frac{N}{d} = D$ )

5260 / 1 = 5260 (the remainder is 0, so 1 and 5260 are divisors of 5260)
5260 / 2 = 2630 (the remainder is 0, so 2 and 2630 are divisors of 5260)
5260 / 3 = 1753.3333333333 (the remainder is 1, so 3 is not a divisor of 5260)
...
5260 / 71 = 74.084507042254 (the remainder is 6, so 71 is not a divisor of 5260)
5260 / 72 = 73.055555555556 (the remainder is 4, so 72 is not a divisor of 5260)