What are the divisors of 1718?

1, 2, 859, 1718

There is a total of 4 positive divisors.
The sum of these divisors is 2580.
The arithmetic mean is 645.

2 even divisors

2, 1718

2 odd divisors

1, 859

How to compute the divisors of 1718?

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 1718 by each of the numbers from 1 to 1718 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)

1718 / 1 = 1718 (the remainder is 0, so 1 is a divisor of 1718)
1718 / 2 = 859 (the remainder is 0, so 2 is a divisor of 1718)
1718 / 3 = 572.66666666667 (the remainder is 2, so 3 is not a divisor of 1718)
...
1718 / 1717 = 1.0005824111823 (the remainder is 1, so 1717 is not a divisor of 1718)
1718 / 1718 = 1 (the remainder is 0, so 1718 is a divisor of 1718)

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 1718 (i.e. 41.448763552125). 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 $\frac{N}{d} = D$ )

1718 / 1 = 1718 (the remainder is 0, so 1 and 1718 are divisors of 1718)
1718 / 2 = 859 (the remainder is 0, so 2 and 859 are divisors of 1718)
1718 / 3 = 572.66666666667 (the remainder is 2, so 3 is not a divisor of 1718)
...
1718 / 40 = 42.95 (the remainder is 38, so 40 is not a divisor of 1718)
1718 / 41 = 41.90243902439 (the remainder is 37, so 41 is not a divisor of 1718)