What are the divisors of 2168?

1, 2, 4, 8, 271, 542, 1084, 2168

There is a total of 8 positive divisors.
The sum of these divisors is 4080.
The arithmetic mean is 510.

6 even divisors

2, 4, 8, 542, 1084, 2168

2 odd divisors

1, 271

How to compute the divisors of 2168?

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 2168 by each of the numbers from 1 to 2168 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)

2168 / 1 = 2168 (the remainder is 0, so 1 is a divisor of 2168)
2168 / 2 = 1084 (the remainder is 0, so 2 is a divisor of 2168)
2168 / 3 = 722.66666666667 (the remainder is 2, so 3 is not a divisor of 2168)
...
2168 / 2167 = 1.0004614674665 (the remainder is 1, so 2167 is not a divisor of 2168)
2168 / 2168 = 1 (the remainder is 0, so 2168 is a divisor of 2168)

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 2168 (i.e. 46.561786907291). 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 $\frac{N}{d} = D$ )

2168 / 1 = 2168 (the remainder is 0, so 1 and 2168 are divisors of 2168)
2168 / 2 = 1084 (the remainder is 0, so 2 and 1084 are divisors of 2168)
2168 / 3 = 722.66666666667 (the remainder is 2, so 3 is not a divisor of 2168)
...
2168 / 45 = 48.177777777778 (the remainder is 8, so 45 is not a divisor of 2168)
2168 / 46 = 47.130434782609 (the remainder is 6, so 46 is not a divisor of 2168)