What are the divisors of 3544?

1, 2, 4, 8, 443, 886, 1772, 3544

There is a total of 8 positive divisors.
The sum of these divisors is 6660.
The arithmetic mean is 832.5.

6 even divisors

2, 4, 8, 886, 1772, 3544

2 odd divisors

1, 443

How to compute the divisors of 3544?

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 3544 by each of the numbers from 1 to 3544 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)

3544 / 1 = 3544 (the remainder is 0, so 1 is a divisor of 3544)
3544 / 2 = 1772 (the remainder is 0, so 2 is a divisor of 3544)
3544 / 3 = 1181.3333333333 (the remainder is 1, so 3 is not a divisor of 3544)
...
3544 / 3543 = 1.0002822466836 (the remainder is 1, so 3543 is not a divisor of 3544)
3544 / 3544 = 1 (the remainder is 0, so 3544 is a divisor of 3544)

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 3544 (i.e. 59.531504264549). 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 $\frac{N}{d} = D$ )

3544 / 1 = 3544 (the remainder is 0, so 1 and 3544 are divisors of 3544)
3544 / 2 = 1772 (the remainder is 0, so 2 and 1772 are divisors of 3544)
3544 / 3 = 1181.3333333333 (the remainder is 1, so 3 is not a divisor of 3544)
...
3544 / 58 = 61.103448275862 (the remainder is 6, so 58 is not a divisor of 3544)
3544 / 59 = 60.067796610169 (the remainder is 4, so 59 is not a divisor of 3544)