What are the divisors of 544?

1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544

There is a total of 12 positive divisors.
The sum of these divisors is 1134.
The arithmetic mean is 94.5.

10 even divisors

2, 4, 8, 16, 32, 34, 68, 136, 272, 544

2 odd divisors

1, 17

How to compute the divisors of 544?

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 544 by each of the numbers from 1 to 544 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)

544 / 1 = 544 (the remainder is 0, so 1 is a divisor of 544)
544 / 2 = 272 (the remainder is 0, so 2 is a divisor of 544)
544 / 3 = 181.33333333333 (the remainder is 1, so 3 is not a divisor of 544)
...
544 / 543 = 1.0018416206262 (the remainder is 1, so 543 is not a divisor of 544)
544 / 544 = 1 (the remainder is 0, so 544 is a divisor of 544)

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 544 (i.e. 23.323807579381). 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 $\frac{N}{d} = D$ )

544 / 1 = 544 (the remainder is 0, so 1 and 544 are divisors of 544)
544 / 2 = 272 (the remainder is 0, so 2 and 272 are divisors of 544)
544 / 3 = 181.33333333333 (the remainder is 1, so 3 is not a divisor of 544)
...
544 / 22 = 24.727272727273 (the remainder is 16, so 22 is not a divisor of 544)
544 / 23 = 23.652173913043 (the remainder is 15, so 23 is not a divisor of 544)