What are the divisors of 5456?

1, 2, 4, 8, 11, 16, 22, 31, 44, 62, 88, 124, 176, 248, 341, 496, 682, 1364, 2728, 5456

There is a total of 20 positive divisors.
The sum of these divisors is 11904.
The arithmetic mean is 595.2.

16 even divisors

2, 4, 8, 16, 22, 44, 62, 88, 124, 176, 248, 496, 682, 1364, 2728, 5456

4 odd divisors

1, 11, 31, 341

How to compute the divisors of 5456?

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 5456 by each of the numbers from 1 to 5456 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)

5456 / 1 = 5456 (the remainder is 0, so 1 is a divisor of 5456)
5456 / 2 = 2728 (the remainder is 0, so 2 is a divisor of 5456)
5456 / 3 = 1818.6666666667 (the remainder is 2, so 3 is not a divisor of 5456)
...
5456 / 5455 = 1.0001833180568 (the remainder is 1, so 5455 is not a divisor of 5456)
5456 / 5456 = 1 (the remainder is 0, so 5456 is a divisor of 5456)

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 5456 (i.e. 73.864741250478). 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 $\frac{N}{d} = D$ )

5456 / 1 = 5456 (the remainder is 0, so 1 and 5456 are divisors of 5456)
5456 / 2 = 2728 (the remainder is 0, so 2 and 2728 are divisors of 5456)
5456 / 3 = 1818.6666666667 (the remainder is 2, so 3 is not a divisor of 5456)
...
5456 / 72 = 75.777777777778 (the remainder is 56, so 72 is not a divisor of 5456)
5456 / 73 = 74.739726027397 (the remainder is 54, so 73 is not a divisor of 5456)