What are the divisors of 508?

1, 2, 4, 127, 254, 508

There is a total of 6 positive divisors.
The sum of these divisors is 896.
The arithmetic mean is 149.33333333333.

4 even divisors

2, 4, 254, 508

2 odd divisors

1, 127

How to compute the divisors of 508?

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 508 by each of the numbers from 1 to 508 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)

508 / 1 = 508 (the remainder is 0, so 1 is a divisor of 508)
508 / 2 = 254 (the remainder is 0, so 2 is a divisor of 508)
508 / 3 = 169.33333333333 (the remainder is 1, so 3 is not a divisor of 508)
...
508 / 507 = 1.0019723865878 (the remainder is 1, so 507 is not a divisor of 508)
508 / 508 = 1 (the remainder is 0, so 508 is a divisor of 508)

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 508 (i.e. 22.538855339169). 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 $\frac{N}{d} = D$ )

508 / 1 = 508 (the remainder is 0, so 1 and 508 are divisors of 508)
508 / 2 = 254 (the remainder is 0, so 2 and 254 are divisors of 508)
508 / 3 = 169.33333333333 (the remainder is 1, so 3 is not a divisor of 508)
...
508 / 21 = 24.190476190476 (the remainder is 4, so 21 is not a divisor of 508)
508 / 22 = 23.090909090909 (the remainder is 2, so 22 is not a divisor of 508)