What are the divisors of 3546?

1, 2, 3, 6, 9, 18, 197, 394, 591, 1182, 1773, 3546

There is a total of 12 positive divisors.
The sum of these divisors is 7722.
The arithmetic mean is 643.5.

6 even divisors

2, 6, 18, 394, 1182, 3546

6 odd divisors

1, 3, 9, 197, 591, 1773

How to compute the divisors of 3546?

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 3546 by each of the numbers from 1 to 3546 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)

3546 / 1 = 3546 (the remainder is 0, so 1 is a divisor of 3546)
3546 / 2 = 1773 (the remainder is 0, so 2 is a divisor of 3546)
3546 / 3 = 1182 (the remainder is 0, so 3 is a divisor of 3546)
...
3546 / 3545 = 1.0002820874471 (the remainder is 1, so 3545 is not a divisor of 3546)
3546 / 3546 = 1 (the remainder is 0, so 3546 is a divisor of 3546)

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 3546 (i.e. 59.548299723838). 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 $\frac{N}{d} = D$ )

3546 / 1 = 3546 (the remainder is 0, so 1 and 3546 are divisors of 3546)
3546 / 2 = 1773 (the remainder is 0, so 2 and 1773 are divisors of 3546)
3546 / 3 = 1182 (the remainder is 0, so 3 and 1182 are divisors of 3546)
...
3546 / 58 = 61.137931034483 (the remainder is 8, so 58 is not a divisor of 3546)
3546 / 59 = 60.101694915254 (the remainder is 6, so 59 is not a divisor of 3546)