What are the divisors of 3541?

1, 3541

There is a total of 2 positive divisors.
The sum of these divisors is 3542.
The arithmetic mean is 1771.

2 odd divisors

1, 3541

How to compute the divisors of 3541?

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 3541 by each of the numbers from 1 to 3541 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)

3541 / 1 = 3541 (the remainder is 0, so 1 is a divisor of 3541)
3541 / 2 = 1770.5 (the remainder is 1, so 2 is not a divisor of 3541)
3541 / 3 = 1180.3333333333 (the remainder is 1, so 3 is not a divisor of 3541)
...
3541 / 3540 = 1.0002824858757 (the remainder is 1, so 3540 is not a divisor of 3541)
3541 / 3541 = 1 (the remainder is 0, so 3541 is a divisor of 3541)

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 3541 (i.e. 59.506302187247). 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 $\frac{N}{d} = D$ )

3541 / 1 = 3541 (the remainder is 0, so 1 and 3541 are divisors of 3541)
3541 / 2 = 1770.5 (the remainder is 1, so 2 is not a divisor of 3541)
3541 / 3 = 1180.3333333333 (the remainder is 1, so 3 is not a divisor of 3541)
...
3541 / 58 = 61.051724137931 (the remainder is 3, so 58 is not a divisor of 3541)
3541 / 59 = 60.016949152542 (the remainder is 1, so 59 is not a divisor of 3541)