What are the divisors of 3159?

1, 3, 9, 13, 27, 39, 81, 117, 243, 351, 1053, 3159

There is a total of 12 positive divisors.
The sum of these divisors is 5096.
The arithmetic mean is 424.66666666667.

12 odd divisors

1, 3, 9, 13, 27, 39, 81, 117, 243, 351, 1053, 3159

How to compute the divisors of 3159?

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 3159 by each of the numbers from 1 to 3159 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)

3159 / 1 = 3159 (the remainder is 0, so 1 is a divisor of 3159)
3159 / 2 = 1579.5 (the remainder is 1, so 2 is not a divisor of 3159)
3159 / 3 = 1053 (the remainder is 0, so 3 is a divisor of 3159)
...
3159 / 3158 = 1.0003166561115 (the remainder is 1, so 3158 is not a divisor of 3159)
3159 / 3159 = 1 (the remainder is 0, so 3159 is a divisor of 3159)

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 3159 (i.e. 56.204981985586). 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 $\frac{N}{d} = D$ )

3159 / 1 = 3159 (the remainder is 0, so 1 and 3159 are divisors of 3159)
3159 / 2 = 1579.5 (the remainder is 1, so 2 is not a divisor of 3159)
3159 / 3 = 1053 (the remainder is 0, so 3 and 1053 are divisors of 3159)
...
3159 / 55 = 57.436363636364 (the remainder is 24, so 55 is not a divisor of 3159)
3159 / 56 = 56.410714285714 (the remainder is 23, so 56 is not a divisor of 3159)