What are the divisors of 3315?

1, 3, 5, 13, 15, 17, 39, 51, 65, 85, 195, 221, 255, 663, 1105, 3315

There is a total of 16 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 378.

16 odd divisors

1, 3, 5, 13, 15, 17, 39, 51, 65, 85, 195, 221, 255, 663, 1105, 3315

How to compute the divisors of 3315?

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 3315 by each of the numbers from 1 to 3315 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)

3315 / 1 = 3315 (the remainder is 0, so 1 is a divisor of 3315)
3315 / 2 = 1657.5 (the remainder is 1, so 2 is not a divisor of 3315)
3315 / 3 = 1105 (the remainder is 0, so 3 is a divisor of 3315)
...
3315 / 3314 = 1.0003017501509 (the remainder is 1, so 3314 is not a divisor of 3315)
3315 / 3315 = 1 (the remainder is 0, so 3315 is a divisor of 3315)

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 3315 (i.e. 57.576036681939). 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 $\frac{N}{d} = D$ )

3315 / 1 = 3315 (the remainder is 0, so 1 and 3315 are divisors of 3315)
3315 / 2 = 1657.5 (the remainder is 1, so 2 is not a divisor of 3315)
3315 / 3 = 1105 (the remainder is 0, so 3 and 1105 are divisors of 3315)
...
3315 / 56 = 59.196428571429 (the remainder is 11, so 56 is not a divisor of 3315)
3315 / 57 = 58.157894736842 (the remainder is 9, so 57 is not a divisor of 3315)