What are the divisors of 5440?

1, 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 64, 68, 80, 85, 136, 160, 170, 272, 320, 340, 544, 680, 1088, 1360, 2720, 5440

There is a total of 28 positive divisors.
The sum of these divisors is 13716.
The arithmetic mean is 489.85714285714.

24 even divisors

2, 4, 8, 10, 16, 20, 32, 34, 40, 64, 68, 80, 136, 160, 170, 272, 320, 340, 544, 680, 1088, 1360, 2720, 5440

4 odd divisors

1, 5, 17, 85

How to compute the divisors of 5440?

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 5440 by each of the numbers from 1 to 5440 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)

5440 / 1 = 5440 (the remainder is 0, so 1 is a divisor of 5440)
5440 / 2 = 2720 (the remainder is 0, so 2 is a divisor of 5440)
5440 / 3 = 1813.3333333333 (the remainder is 1, so 3 is not a divisor of 5440)
...
5440 / 5439 = 1.0001838573267 (the remainder is 1, so 5439 is not a divisor of 5440)
5440 / 5440 = 1 (the remainder is 0, so 5440 is a divisor of 5440)

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 5440 (i.e. 73.756355658343). 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 $\frac{N}{d} = D$ )

5440 / 1 = 5440 (the remainder is 0, so 1 and 5440 are divisors of 5440)
5440 / 2 = 2720 (the remainder is 0, so 2 and 2720 are divisors of 5440)
5440 / 3 = 1813.3333333333 (the remainder is 1, so 3 is not a divisor of 5440)
...
5440 / 72 = 75.555555555556 (the remainder is 40, so 72 is not a divisor of 5440)
5440 / 73 = 74.520547945205 (the remainder is 38, so 73 is not a divisor of 5440)