What are the divisors of 1618?

1, 2, 809, 1618

There is a total of 4 positive divisors.
The sum of these divisors is 2430.
The arithmetic mean is 607.5.

2 even divisors

2, 1618

2 odd divisors

1, 809

How to compute the divisors of 1618?

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 1618 by each of the numbers from 1 to 1618 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)

1618 / 1 = 1618 (the remainder is 0, so 1 is a divisor of 1618)
1618 / 2 = 809 (the remainder is 0, so 2 is a divisor of 1618)
1618 / 3 = 539.33333333333 (the remainder is 1, so 3 is not a divisor of 1618)
...
1618 / 1617 = 1.0006184291899 (the remainder is 1, so 1617 is not a divisor of 1618)
1618 / 1618 = 1 (the remainder is 0, so 1618 is a divisor of 1618)

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 1618 (i.e. 40.224370722238). 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 $\frac{N}{d} = D$ )

1618 / 1 = 1618 (the remainder is 0, so 1 and 1618 are divisors of 1618)
1618 / 2 = 809 (the remainder is 0, so 2 and 809 are divisors of 1618)
1618 / 3 = 539.33333333333 (the remainder is 1, so 3 is not a divisor of 1618)
...
1618 / 39 = 41.487179487179 (the remainder is 19, so 39 is not a divisor of 1618)
1618 / 40 = 40.45 (the remainder is 18, so 40 is not a divisor of 1618)