What are the divisors of 2570?

1, 2, 5, 10, 257, 514, 1285, 2570

There is a total of 8 positive divisors.
The sum of these divisors is 4644.
The arithmetic mean is 580.5.

4 even divisors

2, 10, 514, 2570

4 odd divisors

1, 5, 257, 1285

How to compute the divisors of 2570?

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 2570 by each of the numbers from 1 to 2570 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)

2570 / 1 = 2570 (the remainder is 0, so 1 is a divisor of 2570)
2570 / 2 = 1285 (the remainder is 0, so 2 is a divisor of 2570)
2570 / 3 = 856.66666666667 (the remainder is 2, so 3 is not a divisor of 2570)
...
2570 / 2569 = 1.00038925652 (the remainder is 1, so 2569 is not a divisor of 2570)
2570 / 2570 = 1 (the remainder is 0, so 2570 is a divisor of 2570)

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 2570 (i.e. 50.695167422546). 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 $\frac{N}{d} = D$ )

2570 / 1 = 2570 (the remainder is 0, so 1 and 2570 are divisors of 2570)
2570 / 2 = 1285 (the remainder is 0, so 2 and 1285 are divisors of 2570)
2570 / 3 = 856.66666666667 (the remainder is 2, so 3 is not a divisor of 2570)
...
2570 / 49 = 52.448979591837 (the remainder is 22, so 49 is not a divisor of 2570)
2570 / 50 = 51.4 (the remainder is 20, so 50 is not a divisor of 2570)