What are the divisors of 502?

1, 2, 251, 502

There is a total of 4 positive divisors.
The sum of these divisors is 756.
The arithmetic mean is 189.

2 even divisors

2, 502

2 odd divisors

1, 251

How to compute the divisors of 502?

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 502 by each of the numbers from 1 to 502 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)

502 / 1 = 502 (the remainder is 0, so 1 is a divisor of 502)
502 / 2 = 251 (the remainder is 0, so 2 is a divisor of 502)
502 / 3 = 167.33333333333 (the remainder is 1, so 3 is not a divisor of 502)
...
502 / 501 = 1.001996007984 (the remainder is 1, so 501 is not a divisor of 502)
502 / 502 = 1 (the remainder is 0, so 502 is a divisor of 502)

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 502 (i.e. 22.405356502408). 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 $\frac{N}{d} = D$ )

502 / 1 = 502 (the remainder is 0, so 1 and 502 are divisors of 502)
502 / 2 = 251 (the remainder is 0, so 2 and 251 are divisors of 502)
502 / 3 = 167.33333333333 (the remainder is 1, so 3 is not a divisor of 502)
...
502 / 21 = 23.904761904762 (the remainder is 19, so 21 is not a divisor of 502)
502 / 22 = 22.818181818182 (the remainder is 18, so 22 is not a divisor of 502)