What are the divisors of 1665?

1, 3, 5, 9, 15, 37, 45, 111, 185, 333, 555, 1665

There is a total of 12 positive divisors.
The sum of these divisors is 2964.
The arithmetic mean is 247.

12 odd divisors

1, 3, 5, 9, 15, 37, 45, 111, 185, 333, 555, 1665

How to compute the divisors of 1665?

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 1665 by each of the numbers from 1 to 1665 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)

1665 / 1 = 1665 (the remainder is 0, so 1 is a divisor of 1665)
1665 / 2 = 832.5 (the remainder is 1, so 2 is not a divisor of 1665)
1665 / 3 = 555 (the remainder is 0, so 3 is a divisor of 1665)
...
1665 / 1664 = 1.0006009615385 (the remainder is 1, so 1664 is not a divisor of 1665)
1665 / 1665 = 1 (the remainder is 0, so 1665 is a divisor of 1665)

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 1665 (i.e. 40.804411526206). 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 $\frac{N}{d} = D$ )

1665 / 1 = 1665 (the remainder is 0, so 1 and 1665 are divisors of 1665)
1665 / 2 = 832.5 (the remainder is 1, so 2 is not a divisor of 1665)
1665 / 3 = 555 (the remainder is 0, so 3 and 555 are divisors of 1665)
...
1665 / 39 = 42.692307692308 (the remainder is 27, so 39 is not a divisor of 1665)
1665 / 40 = 41.625 (the remainder is 25, so 40 is not a divisor of 1665)