What are the divisors of 5223?

1, 3, 1741, 5223

There is a total of 4 positive divisors.
The sum of these divisors is 6968.
The arithmetic mean is 1742.

4 odd divisors

1, 3, 1741, 5223

How to compute the divisors of 5223?

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 5223 by each of the numbers from 1 to 5223 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)

5223 / 1 = 5223 (the remainder is 0, so 1 is a divisor of 5223)
5223 / 2 = 2611.5 (the remainder is 1, so 2 is not a divisor of 5223)
5223 / 3 = 1741 (the remainder is 0, so 3 is a divisor of 5223)
...
5223 / 5222 = 1.0001914975105 (the remainder is 1, so 5222 is not a divisor of 5223)
5223 / 5223 = 1 (the remainder is 0, so 5223 is a divisor of 5223)

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 5223 (i.e. 72.270325860619). 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 $\frac{N}{d} = D$ )

5223 / 1 = 5223 (the remainder is 0, so 1 and 5223 are divisors of 5223)
5223 / 2 = 2611.5 (the remainder is 1, so 2 is not a divisor of 5223)
5223 / 3 = 1741 (the remainder is 0, so 3 and 1741 are divisors of 5223)
...
5223 / 71 = 73.56338028169 (the remainder is 40, so 71 is not a divisor of 5223)
5223 / 72 = 72.541666666667 (the remainder is 39, so 72 is not a divisor of 5223)