What are the divisors of 5523?

1, 3, 7, 21, 263, 789, 1841, 5523

There is a total of 8 positive divisors.
The sum of these divisors is 8448.
The arithmetic mean is 1056.

8 odd divisors

1, 3, 7, 21, 263, 789, 1841, 5523

How to compute the divisors of 5523?

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 5523 by each of the numbers from 1 to 5523 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)

5523 / 1 = 5523 (the remainder is 0, so 1 is a divisor of 5523)
5523 / 2 = 2761.5 (the remainder is 1, so 2 is not a divisor of 5523)
5523 / 3 = 1841 (the remainder is 0, so 3 is a divisor of 5523)
...
5523 / 5522 = 1.0001810938066 (the remainder is 1, so 5522 is not a divisor of 5523)
5523 / 5523 = 1 (the remainder is 0, so 5523 is a divisor of 5523)

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 5523 (i.e. 74.316889062985). 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 $\frac{N}{d} = D$ )

5523 / 1 = 5523 (the remainder is 0, so 1 and 5523 are divisors of 5523)
5523 / 2 = 2761.5 (the remainder is 1, so 2 is not a divisor of 5523)
5523 / 3 = 1841 (the remainder is 0, so 3 and 1841 are divisors of 5523)
...
5523 / 73 = 75.657534246575 (the remainder is 48, so 73 is not a divisor of 5523)
5523 / 74 = 74.635135135135 (the remainder is 47, so 74 is not a divisor of 5523)