What are the divisors of 4544?

1, 2, 4, 8, 16, 32, 64, 71, 142, 284, 568, 1136, 2272, 4544

There is a total of 14 positive divisors.
The sum of these divisors is 9144.
The arithmetic mean is 653.14285714286.

12 even divisors

2, 4, 8, 16, 32, 64, 142, 284, 568, 1136, 2272, 4544

2 odd divisors

1, 71

How to compute the divisors of 4544?

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 4544 by each of the numbers from 1 to 4544 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)

4544 / 1 = 4544 (the remainder is 0, so 1 is a divisor of 4544)
4544 / 2 = 2272 (the remainder is 0, so 2 is a divisor of 4544)
4544 / 3 = 1514.6666666667 (the remainder is 2, so 3 is not a divisor of 4544)
...
4544 / 4543 = 1.0002201188642 (the remainder is 1, so 4543 is not a divisor of 4544)
4544 / 4544 = 1 (the remainder is 0, so 4544 is a divisor of 4544)

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 4544 (i.e. 67.409198185411). 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 $\frac{N}{d} = D$ )

4544 / 1 = 4544 (the remainder is 0, so 1 and 4544 are divisors of 4544)
4544 / 2 = 2272 (the remainder is 0, so 2 and 2272 are divisors of 4544)
4544 / 3 = 1514.6666666667 (the remainder is 2, so 3 is not a divisor of 4544)
...
4544 / 66 = 68.848484848485 (the remainder is 56, so 66 is not a divisor of 4544)
4544 / 67 = 67.820895522388 (the remainder is 55, so 67 is not a divisor of 4544)