What are the divisors of 618?

1, 2, 3, 6, 103, 206, 309, 618

There is a total of 8 positive divisors.
The sum of these divisors is 1248.
The arithmetic mean is 156.

4 even divisors

2, 6, 206, 618

4 odd divisors

1, 3, 103, 309

How to compute the divisors of 618?

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 618 by each of the numbers from 1 to 618 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)

618 / 1 = 618 (the remainder is 0, so 1 is a divisor of 618)
618 / 2 = 309 (the remainder is 0, so 2 is a divisor of 618)
618 / 3 = 206 (the remainder is 0, so 3 is a divisor of 618)
...
618 / 617 = 1.0016207455429 (the remainder is 1, so 617 is not a divisor of 618)
618 / 618 = 1 (the remainder is 0, so 618 is a divisor of 618)

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 618 (i.e. 24.859605789312). 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 $\frac{N}{d} = D$ )

618 / 1 = 618 (the remainder is 0, so 1 and 618 are divisors of 618)
618 / 2 = 309 (the remainder is 0, so 2 and 309 are divisors of 618)
618 / 3 = 206 (the remainder is 0, so 3 and 206 are divisors of 618)
...
618 / 23 = 26.869565217391 (the remainder is 20, so 23 is not a divisor of 618)
618 / 24 = 25.75 (the remainder is 18, so 24 is not a divisor of 618)