What are the divisors of 5748?

1, 2, 3, 4, 6, 12, 479, 958, 1437, 1916, 2874, 5748

There is a total of 12 positive divisors.
The sum of these divisors is 13440.
The arithmetic mean is 1120.

8 even divisors

2, 4, 6, 12, 958, 1916, 2874, 5748

4 odd divisors

1, 3, 479, 1437

How to compute the divisors of 5748?

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 5748 by each of the numbers from 1 to 5748 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)

5748 / 1 = 5748 (the remainder is 0, so 1 is a divisor of 5748)
5748 / 2 = 2874 (the remainder is 0, so 2 is a divisor of 5748)
5748 / 3 = 1916 (the remainder is 0, so 3 is a divisor of 5748)
...
5748 / 5747 = 1.0001740038281 (the remainder is 1, so 5747 is not a divisor of 5748)
5748 / 5748 = 1 (the remainder is 0, so 5748 is a divisor of 5748)

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 5748 (i.e. 75.815565684099). 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 $\frac{N}{d} = D$ )

5748 / 1 = 5748 (the remainder is 0, so 1 and 5748 are divisors of 5748)
5748 / 2 = 2874 (the remainder is 0, so 2 and 2874 are divisors of 5748)
5748 / 3 = 1916 (the remainder is 0, so 3 and 1916 are divisors of 5748)
...
5748 / 74 = 77.675675675676 (the remainder is 50, so 74 is not a divisor of 5748)
5748 / 75 = 76.64 (the remainder is 48, so 75 is not a divisor of 5748)