What are the divisors of 3106?

1, 2, 1553, 3106

There is a total of 4 positive divisors.
The sum of these divisors is 4662.
The arithmetic mean is 1165.5.

2 even divisors

2, 3106

2 odd divisors

1, 1553

How to compute the divisors of 3106?

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 3106 by each of the numbers from 1 to 3106 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)

3106 / 1 = 3106 (the remainder is 0, so 1 is a divisor of 3106)
3106 / 2 = 1553 (the remainder is 0, so 2 is a divisor of 3106)
3106 / 3 = 1035.3333333333 (the remainder is 1, so 3 is not a divisor of 3106)
...
3106 / 3105 = 1.0003220611916 (the remainder is 1, so 3105 is not a divisor of 3106)
3106 / 3106 = 1 (the remainder is 0, so 3106 is a divisor of 3106)

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 3106 (i.e. 55.731499172371). 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 $\frac{N}{d} = D$ )

3106 / 1 = 3106 (the remainder is 0, so 1 and 3106 are divisors of 3106)
3106 / 2 = 1553 (the remainder is 0, so 2 and 1553 are divisors of 3106)
3106 / 3 = 1035.3333333333 (the remainder is 1, so 3 is not a divisor of 3106)
...
3106 / 54 = 57.518518518519 (the remainder is 28, so 54 is not a divisor of 3106)
3106 / 55 = 56.472727272727 (the remainder is 26, so 55 is not a divisor of 3106)