What are the divisors of 2569?

1, 7, 367, 2569

There is a total of 4 positive divisors.
The sum of these divisors is 2944.
The arithmetic mean is 736.

4 odd divisors

1, 7, 367, 2569

How to compute the divisors of 2569?

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 2569 by each of the numbers from 1 to 2569 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)

2569 / 1 = 2569 (the remainder is 0, so 1 is a divisor of 2569)
2569 / 2 = 1284.5 (the remainder is 1, so 2 is not a divisor of 2569)
2569 / 3 = 856.33333333333 (the remainder is 1, so 3 is not a divisor of 2569)
...
2569 / 2568 = 1.0003894080997 (the remainder is 1, so 2568 is not a divisor of 2569)
2569 / 2569 = 1 (the remainder is 0, so 2569 is a divisor of 2569)

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 2569 (i.e. 50.685303589897). 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 $\frac{N}{d} = D$ )

2569 / 1 = 2569 (the remainder is 0, so 1 and 2569 are divisors of 2569)
2569 / 2 = 1284.5 (the remainder is 1, so 2 is not a divisor of 2569)
2569 / 3 = 856.33333333333 (the remainder is 1, so 3 is not a divisor of 2569)
...
2569 / 49 = 52.428571428571 (the remainder is 21, so 49 is not a divisor of 2569)
2569 / 50 = 51.38 (the remainder is 19, so 50 is not a divisor of 2569)