What are the divisors of 587?

1, 587

There is a total of 2 positive divisors.
The sum of these divisors is 588.
The arithmetic mean is 294.

2 odd divisors

1, 587

How to compute the divisors of 587?

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 587 by each of the numbers from 1 to 587 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)

587 / 1 = 587 (the remainder is 0, so 1 is a divisor of 587)
587 / 2 = 293.5 (the remainder is 1, so 2 is not a divisor of 587)
587 / 3 = 195.66666666667 (the remainder is 2, so 3 is not a divisor of 587)
...
587 / 586 = 1.0017064846416 (the remainder is 1, so 586 is not a divisor of 587)
587 / 587 = 1 (the remainder is 0, so 587 is a divisor of 587)

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 587 (i.e. 24.228082879171). 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 $\frac{N}{d} = D$ )

587 / 1 = 587 (the remainder is 0, so 1 and 587 are divisors of 587)
587 / 2 = 293.5 (the remainder is 1, so 2 is not a divisor of 587)
587 / 3 = 195.66666666667 (the remainder is 2, so 3 is not a divisor of 587)
...
587 / 23 = 25.521739130435 (the remainder is 12, so 23 is not a divisor of 587)
587 / 24 = 24.458333333333 (the remainder is 11, so 24 is not a divisor of 587)