What are the divisors of 5226?

1, 2, 3, 6, 13, 26, 39, 67, 78, 134, 201, 402, 871, 1742, 2613, 5226

There is a total of 16 positive divisors.
The sum of these divisors is 11424.
The arithmetic mean is 714.

8 even divisors

2, 6, 26, 78, 134, 402, 1742, 5226

8 odd divisors

1, 3, 13, 39, 67, 201, 871, 2613

How to compute the divisors of 5226?

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 5226 by each of the numbers from 1 to 5226 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)

5226 / 1 = 5226 (the remainder is 0, so 1 is a divisor of 5226)
5226 / 2 = 2613 (the remainder is 0, so 2 is a divisor of 5226)
5226 / 3 = 1742 (the remainder is 0, so 3 is a divisor of 5226)
...
5226 / 5225 = 1.0001913875598 (the remainder is 1, so 5225 is not a divisor of 5226)
5226 / 5226 = 1 (the remainder is 0, so 5226 is a divisor of 5226)

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 5226 (i.e. 72.291078287711). 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 $\frac{N}{d} = D$ )

5226 / 1 = 5226 (the remainder is 0, so 1 and 5226 are divisors of 5226)
5226 / 2 = 2613 (the remainder is 0, so 2 and 2613 are divisors of 5226)
5226 / 3 = 1742 (the remainder is 0, so 3 and 1742 are divisors of 5226)
...
5226 / 71 = 73.605633802817 (the remainder is 43, so 71 is not a divisor of 5226)
5226 / 72 = 72.583333333333 (the remainder is 42, so 72 is not a divisor of 5226)