What are the divisors of 185?

1, 5, 37, 185

There is a total of 4 positive divisors.
The sum of these divisors is 228.
The arithmetic mean is 57.

4 odd divisors

1, 5, 37, 185

How to compute the divisors of 185?

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 185 by each of the numbers from 1 to 185 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)

185 / 1 = 185 (the remainder is 0, so 1 is a divisor of 185)
185 / 2 = 92.5 (the remainder is 1, so 2 is not a divisor of 185)
185 / 3 = 61.666666666667 (the remainder is 2, so 3 is not a divisor of 185)
...
185 / 184 = 1.0054347826087 (the remainder is 1, so 184 is not a divisor of 185)
185 / 185 = 1 (the remainder is 0, so 185 is a divisor of 185)

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 185 (i.e. 13.601470508735). 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 $\frac{N}{d} = D$ )

185 / 1 = 185 (the remainder is 0, so 1 and 185 are divisors of 185)
185 / 2 = 92.5 (the remainder is 1, so 2 is not a divisor of 185)
185 / 3 = 61.666666666667 (the remainder is 2, so 3 is not a divisor of 185)
...
185 / 12 = 15.416666666667 (the remainder is 5, so 12 is not a divisor of 185)
185 / 13 = 14.230769230769 (the remainder is 3, so 13 is not a divisor of 185)