What are the divisors of 3285?

1, 3, 5, 9, 15, 45, 73, 219, 365, 657, 1095, 3285

There is a total of 12 positive divisors.
The sum of these divisors is 5772.
The arithmetic mean is 481.

12 odd divisors

1, 3, 5, 9, 15, 45, 73, 219, 365, 657, 1095, 3285

How to compute the divisors of 3285?

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 3285 by each of the numbers from 1 to 3285 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)

3285 / 1 = 3285 (the remainder is 0, so 1 is a divisor of 3285)
3285 / 2 = 1642.5 (the remainder is 1, so 2 is not a divisor of 3285)
3285 / 3 = 1095 (the remainder is 0, so 3 is a divisor of 3285)
...
3285 / 3284 = 1.0003045066991 (the remainder is 1, so 3284 is not a divisor of 3285)
3285 / 3285 = 1 (the remainder is 0, so 3285 is a divisor of 3285)

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 3285 (i.e. 57.314919523628). 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 $\frac{N}{d} = D$ )

3285 / 1 = 3285 (the remainder is 0, so 1 and 3285 are divisors of 3285)
3285 / 2 = 1642.5 (the remainder is 1, so 2 is not a divisor of 3285)
3285 / 3 = 1095 (the remainder is 0, so 3 and 1095 are divisors of 3285)
...
3285 / 56 = 58.660714285714 (the remainder is 37, so 56 is not a divisor of 3285)
3285 / 57 = 57.631578947368 (the remainder is 36, so 57 is not a divisor of 3285)