What are the divisors of 5268?

1, 2, 3, 4, 6, 12, 439, 878, 1317, 1756, 2634, 5268

There is a total of 12 positive divisors.
The sum of these divisors is 12320.
The arithmetic mean is 1026.6666666667.

8 even divisors

2, 4, 6, 12, 878, 1756, 2634, 5268

4 odd divisors

1, 3, 439, 1317

How to compute the divisors of 5268?

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 5268 by each of the numbers from 1 to 5268 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)

5268 / 1 = 5268 (the remainder is 0, so 1 is a divisor of 5268)
5268 / 2 = 2634 (the remainder is 0, so 2 is a divisor of 5268)
5268 / 3 = 1756 (the remainder is 0, so 3 is a divisor of 5268)
...
5268 / 5267 = 1.0001898614012 (the remainder is 1, so 5267 is not a divisor of 5268)
5268 / 5268 = 1 (the remainder is 0, so 5268 is a divisor of 5268)

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 5268 (i.e. 72.580989246496). 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 $\frac{N}{d} = D$ )

5268 / 1 = 5268 (the remainder is 0, so 1 and 5268 are divisors of 5268)
5268 / 2 = 2634 (the remainder is 0, so 2 and 2634 are divisors of 5268)
5268 / 3 = 1756 (the remainder is 0, so 3 and 1756 are divisors of 5268)
...
5268 / 71 = 74.197183098592 (the remainder is 14, so 71 is not a divisor of 5268)
5268 / 72 = 73.166666666667 (the remainder is 12, so 72 is not a divisor of 5268)