What are the divisors of 5324?

1, 2, 4, 11, 22, 44, 121, 242, 484, 1331, 2662, 5324

There is a total of 12 positive divisors.
The sum of these divisors is 10248.
The arithmetic mean is 854.

8 even divisors

2, 4, 22, 44, 242, 484, 2662, 5324

4 odd divisors

1, 11, 121, 1331

How to compute the divisors of 5324?

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 5324 by each of the numbers from 1 to 5324 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)

5324 / 1 = 5324 (the remainder is 0, so 1 is a divisor of 5324)
5324 / 2 = 2662 (the remainder is 0, so 2 is a divisor of 5324)
5324 / 3 = 1774.6666666667 (the remainder is 2, so 3 is not a divisor of 5324)
...
5324 / 5323 = 1.0001878639865 (the remainder is 1, so 5323 is not a divisor of 5324)
5324 / 5324 = 1 (the remainder is 0, so 5324 is a divisor of 5324)

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 5324 (i.e. 72.965745387819). 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 $\frac{N}{d} = D$ )

5324 / 1 = 5324 (the remainder is 0, so 1 and 5324 are divisors of 5324)
5324 / 2 = 2662 (the remainder is 0, so 2 and 2662 are divisors of 5324)
5324 / 3 = 1774.6666666667 (the remainder is 2, so 3 is not a divisor of 5324)
...
5324 / 71 = 74.985915492958 (the remainder is 70, so 71 is not a divisor of 5324)
5324 / 72 = 73.944444444444 (the remainder is 68, so 72 is not a divisor of 5324)