What are the divisors of 2581?

1, 29, 89, 2581

There is a total of 4 positive divisors.
The sum of these divisors is 2700.
The arithmetic mean is 675.

4 odd divisors

1, 29, 89, 2581

How to compute the divisors of 2581?

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 2581 by each of the numbers from 1 to 2581 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)

2581 / 1 = 2581 (the remainder is 0, so 1 is a divisor of 2581)
2581 / 2 = 1290.5 (the remainder is 1, so 2 is not a divisor of 2581)
2581 / 3 = 860.33333333333 (the remainder is 1, so 3 is not a divisor of 2581)
...
2581 / 2580 = 1.0003875968992 (the remainder is 1, so 2580 is not a divisor of 2581)
2581 / 2581 = 1 (the remainder is 0, so 2581 is a divisor of 2581)

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 2581 (i.e. 50.803543183522). 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 $\frac{N}{d} = D$ )

2581 / 1 = 2581 (the remainder is 0, so 1 and 2581 are divisors of 2581)
2581 / 2 = 1290.5 (the remainder is 1, so 2 is not a divisor of 2581)
2581 / 3 = 860.33333333333 (the remainder is 1, so 3 is not a divisor of 2581)
...
2581 / 49 = 52.673469387755 (the remainder is 33, so 49 is not a divisor of 2581)
2581 / 50 = 51.62 (the remainder is 31, so 50 is not a divisor of 2581)