What are the divisors of 3549?

1, 3, 7, 13, 21, 39, 91, 169, 273, 507, 1183, 3549

There is a total of 12 positive divisors.
The sum of these divisors is 5856.
The arithmetic mean is 488.

12 odd divisors

1, 3, 7, 13, 21, 39, 91, 169, 273, 507, 1183, 3549

How to compute the divisors of 3549?

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 3549 by each of the numbers from 1 to 3549 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)

3549 / 1 = 3549 (the remainder is 0, so 1 is a divisor of 3549)
3549 / 2 = 1774.5 (the remainder is 1, so 2 is not a divisor of 3549)
3549 / 3 = 1183 (the remainder is 0, so 3 is a divisor of 3549)
...
3549 / 3548 = 1.000281848929 (the remainder is 1, so 3548 is not a divisor of 3549)
3549 / 3549 = 1 (the remainder is 0, so 3549 is a divisor of 3549)

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 3549 (i.e. 59.573484034426). 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 $\frac{N}{d} = D$ )

3549 / 1 = 3549 (the remainder is 0, so 1 and 3549 are divisors of 3549)
3549 / 2 = 1774.5 (the remainder is 1, so 2 is not a divisor of 3549)
3549 / 3 = 1183 (the remainder is 0, so 3 and 1183 are divisors of 3549)
...
3549 / 58 = 61.189655172414 (the remainder is 11, so 58 is not a divisor of 3549)
3549 / 59 = 60.152542372881 (the remainder is 9, so 59 is not a divisor of 3549)