What are the divisors of 3569?

1, 43, 83, 3569

There is a total of 4 positive divisors.
The sum of these divisors is 3696.
The arithmetic mean is 924.

4 odd divisors

1, 43, 83, 3569

How to compute the divisors of 3569?

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 3569 by each of the numbers from 1 to 3569 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)

3569 / 1 = 3569 (the remainder is 0, so 1 is a divisor of 3569)
3569 / 2 = 1784.5 (the remainder is 1, so 2 is not a divisor of 3569)
3569 / 3 = 1189.6666666667 (the remainder is 2, so 3 is not a divisor of 3569)
...
3569 / 3568 = 1.0002802690583 (the remainder is 1, so 3568 is not a divisor of 3569)
3569 / 3569 = 1 (the remainder is 0, so 3569 is a divisor of 3569)

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 3569 (i.e. 59.741108124975). 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 $\frac{N}{d} = D$ )

3569 / 1 = 3569 (the remainder is 0, so 1 and 3569 are divisors of 3569)
3569 / 2 = 1784.5 (the remainder is 1, so 2 is not a divisor of 3569)
3569 / 3 = 1189.6666666667 (the remainder is 2, so 3 is not a divisor of 3569)
...
3569 / 58 = 61.534482758621 (the remainder is 31, so 58 is not a divisor of 3569)
3569 / 59 = 60.491525423729 (the remainder is 29, so 59 is not a divisor of 3569)