What are the divisors of 3539?

1, 3539

There is a total of 2 positive divisors.
The sum of these divisors is 3540.
The arithmetic mean is 1770.

2 odd divisors

1, 3539

How to compute the divisors of 3539?

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 3539 by each of the numbers from 1 to 3539 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)

3539 / 1 = 3539 (the remainder is 0, so 1 is a divisor of 3539)
3539 / 2 = 1769.5 (the remainder is 1, so 2 is not a divisor of 3539)
3539 / 3 = 1179.6666666667 (the remainder is 2, so 3 is not a divisor of 3539)
...
3539 / 3538 = 1.0002826455625 (the remainder is 1, so 3538 is not a divisor of 3539)
3539 / 3539 = 1 (the remainder is 0, so 3539 is a divisor of 3539)

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 3539 (i.e. 59.489494870943). 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 $\frac{N}{d} = D$ )

3539 / 1 = 3539 (the remainder is 0, so 1 and 3539 are divisors of 3539)
3539 / 2 = 1769.5 (the remainder is 1, so 2 is not a divisor of 3539)
3539 / 3 = 1179.6666666667 (the remainder is 2, so 3 is not a divisor of 3539)
...
3539 / 58 = 61.01724137931 (the remainder is 1, so 58 is not a divisor of 3539)
3539 / 59 = 59.983050847458 (the remainder is 58, so 59 is not a divisor of 3539)