What are the divisors of 2185?

1, 5, 19, 23, 95, 115, 437, 2185

There is a total of 8 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 360.

8 odd divisors

1, 5, 19, 23, 95, 115, 437, 2185

How to compute the divisors of 2185?

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 2185 by each of the numbers from 1 to 2185 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)

2185 / 1 = 2185 (the remainder is 0, so 1 is a divisor of 2185)
2185 / 2 = 1092.5 (the remainder is 1, so 2 is not a divisor of 2185)
2185 / 3 = 728.33333333333 (the remainder is 1, so 3 is not a divisor of 2185)
...
2185 / 2184 = 1.0004578754579 (the remainder is 1, so 2184 is not a divisor of 2185)
2185 / 2185 = 1 (the remainder is 0, so 2185 is a divisor of 2185)

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 2185 (i.e. 46.743983570081). 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 $\frac{N}{d} = D$ )

2185 / 1 = 2185 (the remainder is 0, so 1 and 2185 are divisors of 2185)
2185 / 2 = 1092.5 (the remainder is 1, so 2 is not a divisor of 2185)
2185 / 3 = 728.33333333333 (the remainder is 1, so 3 is not a divisor of 2185)
...
2185 / 45 = 48.555555555556 (the remainder is 25, so 45 is not a divisor of 2185)
2185 / 46 = 47.5 (the remainder is 23, so 46 is not a divisor of 2185)