What are the divisors of 584?

1, 2, 4, 8, 73, 146, 292, 584

There is a total of 8 positive divisors.
The sum of these divisors is 1110.
The arithmetic mean is 138.75.

6 even divisors

2, 4, 8, 146, 292, 584

2 odd divisors

1, 73

How to compute the divisors of 584?

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 584 by each of the numbers from 1 to 584 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)

584 / 1 = 584 (the remainder is 0, so 1 is a divisor of 584)
584 / 2 = 292 (the remainder is 0, so 2 is a divisor of 584)
584 / 3 = 194.66666666667 (the remainder is 2, so 3 is not a divisor of 584)
...
584 / 583 = 1.0017152658662 (the remainder is 1, so 583 is not a divisor of 584)
584 / 584 = 1 (the remainder is 0, so 584 is a divisor of 584)

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 584 (i.e. 24.166091947189). 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 $\frac{N}{d} = D$ )

584 / 1 = 584 (the remainder is 0, so 1 and 584 are divisors of 584)
584 / 2 = 292 (the remainder is 0, so 2 and 292 are divisors of 584)
584 / 3 = 194.66666666667 (the remainder is 2, so 3 is not a divisor of 584)
...
584 / 23 = 25.391304347826 (the remainder is 9, so 23 is not a divisor of 584)
584 / 24 = 24.333333333333 (the remainder is 8, so 24 is not a divisor of 584)