What are the divisors of 5744?

1, 2, 4, 8, 16, 359, 718, 1436, 2872, 5744

There is a total of 10 positive divisors.
The sum of these divisors is 11160.
The arithmetic mean is 1116.

8 even divisors

2, 4, 8, 16, 718, 1436, 2872, 5744

2 odd divisors

1, 359

How to compute the divisors of 5744?

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 5744 by each of the numbers from 1 to 5744 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)

5744 / 1 = 5744 (the remainder is 0, so 1 is a divisor of 5744)
5744 / 2 = 2872 (the remainder is 0, so 2 is a divisor of 5744)
5744 / 3 = 1914.6666666667 (the remainder is 2, so 3 is not a divisor of 5744)
...
5744 / 5743 = 1.0001741250218 (the remainder is 1, so 5743 is not a divisor of 5744)
5744 / 5744 = 1 (the remainder is 0, so 5744 is a divisor of 5744)

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 5744 (i.e. 75.789181285986). 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 $\frac{N}{d} = D$ )

5744 / 1 = 5744 (the remainder is 0, so 1 and 5744 are divisors of 5744)
5744 / 2 = 2872 (the remainder is 0, so 2 and 2872 are divisors of 5744)
5744 / 3 = 1914.6666666667 (the remainder is 2, so 3 is not a divisor of 5744)
...
5744 / 74 = 77.621621621622 (the remainder is 46, so 74 is not a divisor of 5744)
5744 / 75 = 76.586666666667 (the remainder is 44, so 75 is not a divisor of 5744)