What are the divisors of 3559?

1, 3559

There is a total of 2 positive divisors.
The sum of these divisors is 3560.
The arithmetic mean is 1780.

2 odd divisors

1, 3559

How to compute the divisors of 3559?

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 3559 by each of the numbers from 1 to 3559 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)

3559 / 1 = 3559 (the remainder is 0, so 1 is a divisor of 3559)
3559 / 2 = 1779.5 (the remainder is 1, so 2 is not a divisor of 3559)
3559 / 3 = 1186.3333333333 (the remainder is 1, so 3 is not a divisor of 3559)
...
3559 / 3558 = 1.0002810567735 (the remainder is 1, so 3558 is not a divisor of 3559)
3559 / 3559 = 1 (the remainder is 0, so 3559 is a divisor of 3559)

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 3559 (i.e. 59.657354953099). 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 $\frac{N}{d} = D$ )

3559 / 1 = 3559 (the remainder is 0, so 1 and 3559 are divisors of 3559)
3559 / 2 = 1779.5 (the remainder is 1, so 2 is not a divisor of 3559)
3559 / 3 = 1186.3333333333 (the remainder is 1, so 3 is not a divisor of 3559)
...
3559 / 58 = 61.362068965517 (the remainder is 21, so 58 is not a divisor of 3559)
3559 / 59 = 60.322033898305 (the remainder is 19, so 59 is not a divisor of 3559)