What are the divisors of 581?

1, 7, 83, 581

There is a total of 4 positive divisors.
The sum of these divisors is 672.
The arithmetic mean is 168.

4 odd divisors

1, 7, 83, 581

How to compute the divisors of 581?

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 581 by each of the numbers from 1 to 581 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)

581 / 1 = 581 (the remainder is 0, so 1 is a divisor of 581)
581 / 2 = 290.5 (the remainder is 1, so 2 is not a divisor of 581)
581 / 3 = 193.66666666667 (the remainder is 2, so 3 is not a divisor of 581)
...
581 / 580 = 1.001724137931 (the remainder is 1, so 580 is not a divisor of 581)
581 / 581 = 1 (the remainder is 0, so 581 is a divisor of 581)

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 581 (i.e. 24.103941586388). 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 $\frac{N}{d} = D$ )

581 / 1 = 581 (the remainder is 0, so 1 and 581 are divisors of 581)
581 / 2 = 290.5 (the remainder is 1, so 2 is not a divisor of 581)
581 / 3 = 193.66666666667 (the remainder is 2, so 3 is not a divisor of 581)
...
581 / 23 = 25.260869565217 (the remainder is 6, so 23 is not a divisor of 581)
581 / 24 = 24.208333333333 (the remainder is 5, so 24 is not a divisor of 581)