What are the divisors of 2583?

1, 3, 7, 9, 21, 41, 63, 123, 287, 369, 861, 2583

There is a total of 12 positive divisors.
The sum of these divisors is 4368.
The arithmetic mean is 364.

12 odd divisors

1, 3, 7, 9, 21, 41, 63, 123, 287, 369, 861, 2583

How to compute the divisors of 2583?

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 2583 by each of the numbers from 1 to 2583 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)

2583 / 1 = 2583 (the remainder is 0, so 1 is a divisor of 2583)
2583 / 2 = 1291.5 (the remainder is 1, so 2 is not a divisor of 2583)
2583 / 3 = 861 (the remainder is 0, so 3 is a divisor of 2583)
...
2583 / 2582 = 1.0003872966692 (the remainder is 1, so 2582 is not a divisor of 2583)
2583 / 2583 = 1 (the remainder is 0, so 2583 is a divisor of 2583)

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 2583 (i.e. 50.823223038292). 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 $\frac{N}{d} = D$ )

2583 / 1 = 2583 (the remainder is 0, so 1 and 2583 are divisors of 2583)
2583 / 2 = 1291.5 (the remainder is 1, so 2 is not a divisor of 2583)
2583 / 3 = 861 (the remainder is 0, so 3 and 861 are divisors of 2583)
...
2583 / 49 = 52.714285714286 (the remainder is 35, so 49 is not a divisor of 2583)
2583 / 50 = 51.66 (the remainder is 33, so 50 is not a divisor of 2583)