What are the divisors of 3069?

1, 3, 9, 11, 31, 33, 93, 99, 279, 341, 1023, 3069

There is a total of 12 positive divisors.
The sum of these divisors is 4992.
The arithmetic mean is 416.

12 odd divisors

1, 3, 9, 11, 31, 33, 93, 99, 279, 341, 1023, 3069

How to compute the divisors of 3069?

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 3069 by each of the numbers from 1 to 3069 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)

3069 / 1 = 3069 (the remainder is 0, so 1 is a divisor of 3069)
3069 / 2 = 1534.5 (the remainder is 1, so 2 is not a divisor of 3069)
3069 / 3 = 1023 (the remainder is 0, so 3 is a divisor of 3069)
...
3069 / 3068 = 1.0003259452412 (the remainder is 1, so 3068 is not a divisor of 3069)
3069 / 3069 = 1 (the remainder is 0, so 3069 is a divisor of 3069)

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 3069 (i.e. 55.398555937858). 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 $\frac{N}{d} = D$ )

3069 / 1 = 3069 (the remainder is 0, so 1 and 3069 are divisors of 3069)
3069 / 2 = 1534.5 (the remainder is 1, so 2 is not a divisor of 3069)
3069 / 3 = 1023 (the remainder is 0, so 3 and 1023 are divisors of 3069)
...
3069 / 54 = 56.833333333333 (the remainder is 45, so 54 is not a divisor of 3069)
3069 / 55 = 55.8 (the remainder is 44, so 55 is not a divisor of 3069)