What are the divisors of 2566?

1, 2, 1283, 2566

There is a total of 4 positive divisors.
The sum of these divisors is 3852.
The arithmetic mean is 963.

2 even divisors

2, 2566

2 odd divisors

1, 1283

How to compute the divisors of 2566?

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 2566 by each of the numbers from 1 to 2566 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)

2566 / 1 = 2566 (the remainder is 0, so 1 is a divisor of 2566)
2566 / 2 = 1283 (the remainder is 0, so 2 is a divisor of 2566)
2566 / 3 = 855.33333333333 (the remainder is 1, so 3 is not a divisor of 2566)
...
2566 / 2565 = 1.0003898635478 (the remainder is 1, so 2565 is not a divisor of 2566)
2566 / 2566 = 1 (the remainder is 0, so 2566 is a divisor of 2566)

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 2566 (i.e. 50.655700567656). 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 $\frac{N}{d} = D$ )

2566 / 1 = 2566 (the remainder is 0, so 1 and 2566 are divisors of 2566)
2566 / 2 = 1283 (the remainder is 0, so 2 and 1283 are divisors of 2566)
2566 / 3 = 855.33333333333 (the remainder is 1, so 3 is not a divisor of 2566)
...
2566 / 49 = 52.367346938776 (the remainder is 18, so 49 is not a divisor of 2566)
2566 / 50 = 51.32 (the remainder is 16, so 50 is not a divisor of 2566)