What are the divisors of 3543?

1, 3, 1181, 3543

There is a total of 4 positive divisors.
The sum of these divisors is 4728.
The arithmetic mean is 1182.

4 odd divisors

1, 3, 1181, 3543

How to compute the divisors of 3543?

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 3543 by each of the numbers from 1 to 3543 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)

3543 / 1 = 3543 (the remainder is 0, so 1 is a divisor of 3543)
3543 / 2 = 1771.5 (the remainder is 1, so 2 is not a divisor of 3543)
3543 / 3 = 1181 (the remainder is 0, so 3 is a divisor of 3543)
...
3543 / 3542 = 1.0002823263693 (the remainder is 1, so 3542 is not a divisor of 3543)
3543 / 3543 = 1 (the remainder is 0, so 3543 is a divisor of 3543)

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 3543 (i.e. 59.523104757733). 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 $\frac{N}{d} = D$ )

3543 / 1 = 3543 (the remainder is 0, so 1 and 3543 are divisors of 3543)
3543 / 2 = 1771.5 (the remainder is 1, so 2 is not a divisor of 3543)
3543 / 3 = 1181 (the remainder is 0, so 3 and 1181 are divisors of 3543)
...
3543 / 58 = 61.086206896552 (the remainder is 5, so 58 is not a divisor of 3543)
3543 / 59 = 60.050847457627 (the remainder is 3, so 59 is not a divisor of 3543)