What are the divisors of 718?

1, 2, 359, 718

There is a total of 4 positive divisors.
The sum of these divisors is 1080.
The arithmetic mean is 270.

2 even divisors

2, 718

2 odd divisors

1, 359

How to compute the divisors of 718?

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 718 by each of the numbers from 1 to 718 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)

718 / 1 = 718 (the remainder is 0, so 1 is a divisor of 718)
718 / 2 = 359 (the remainder is 0, so 2 is a divisor of 718)
718 / 3 = 239.33333333333 (the remainder is 1, so 3 is not a divisor of 718)
...
718 / 717 = 1.0013947001395 (the remainder is 1, so 717 is not a divisor of 718)
718 / 718 = 1 (the remainder is 0, so 718 is a divisor of 718)

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 718 (i.e. 26.795522013949). 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 $\frac{N}{d} = D$ )

718 / 1 = 718 (the remainder is 0, so 1 and 718 are divisors of 718)
718 / 2 = 359 (the remainder is 0, so 2 and 359 are divisors of 718)
718 / 3 = 239.33333333333 (the remainder is 1, so 3 is not a divisor of 718)
...
718 / 25 = 28.72 (the remainder is 18, so 25 is not a divisor of 718)
718 / 26 = 27.615384615385 (the remainder is 16, so 26 is not a divisor of 718)