What are the divisors of 507?

1, 3, 13, 39, 169, 507

There is a total of 6 positive divisors.
The sum of these divisors is 732.
The arithmetic mean is 122.

6 odd divisors

1, 3, 13, 39, 169, 507

How to compute the divisors of 507?

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 507 by each of the numbers from 1 to 507 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)

507 / 1 = 507 (the remainder is 0, so 1 is a divisor of 507)
507 / 2 = 253.5 (the remainder is 1, so 2 is not a divisor of 507)
507 / 3 = 169 (the remainder is 0, so 3 is a divisor of 507)
...
507 / 506 = 1.001976284585 (the remainder is 1, so 506 is not a divisor of 507)
507 / 507 = 1 (the remainder is 0, so 507 is a divisor of 507)

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 507 (i.e. 22.516660498395). 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 $\frac{N}{d} = D$ )

507 / 1 = 507 (the remainder is 0, so 1 and 507 are divisors of 507)
507 / 2 = 253.5 (the remainder is 1, so 2 is not a divisor of 507)
507 / 3 = 169 (the remainder is 0, so 3 and 169 are divisors of 507)
...
507 / 21 = 24.142857142857 (the remainder is 3, so 21 is not a divisor of 507)
507 / 22 = 23.045454545455 (the remainder is 1, so 22 is not a divisor of 507)