What are the divisors of 2186?

1, 2, 1093, 2186

There is a total of 4 positive divisors.
The sum of these divisors is 3282.
The arithmetic mean is 820.5.

2 even divisors

2, 2186

2 odd divisors

1, 1093

How to compute the divisors of 2186?

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 2186 by each of the numbers from 1 to 2186 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)

2186 / 1 = 2186 (the remainder is 0, so 1 is a divisor of 2186)
2186 / 2 = 1093 (the remainder is 0, so 2 is a divisor of 2186)
2186 / 3 = 728.66666666667 (the remainder is 2, so 3 is not a divisor of 2186)
...
2186 / 2185 = 1.0004576659039 (the remainder is 1, so 2185 is not a divisor of 2186)
2186 / 2186 = 1 (the remainder is 0, so 2186 is a divisor of 2186)

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 2186 (i.e. 46.754678910244). 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 $\frac{N}{d} = D$ )

2186 / 1 = 2186 (the remainder is 0, so 1 and 2186 are divisors of 2186)
2186 / 2 = 1093 (the remainder is 0, so 2 and 1093 are divisors of 2186)
2186 / 3 = 728.66666666667 (the remainder is 2, so 3 is not a divisor of 2186)
...
2186 / 45 = 48.577777777778 (the remainder is 26, so 45 is not a divisor of 2186)
2186 / 46 = 47.521739130435 (the remainder is 24, so 46 is not a divisor of 2186)