What are the divisors of 3094?

1, 2, 7, 13, 14, 17, 26, 34, 91, 119, 182, 221, 238, 442, 1547, 3094

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

8 even divisors

2, 14, 26, 34, 182, 238, 442, 3094

8 odd divisors

1, 7, 13, 17, 91, 119, 221, 1547

How to compute the divisors of 3094?

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 3094 by each of the numbers from 1 to 3094 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)

3094 / 1 = 3094 (the remainder is 0, so 1 is a divisor of 3094)
3094 / 2 = 1547 (the remainder is 0, so 2 is a divisor of 3094)
3094 / 3 = 1031.3333333333 (the remainder is 1, so 3 is not a divisor of 3094)
...
3094 / 3093 = 1.0003233107016 (the remainder is 1, so 3093 is not a divisor of 3094)
3094 / 3094 = 1 (the remainder is 0, so 3094 is a divisor of 3094)

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 3094 (i.e. 55.623735940694). 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 $\frac{N}{d} = D$ )

3094 / 1 = 3094 (the remainder is 0, so 1 and 3094 are divisors of 3094)
3094 / 2 = 1547 (the remainder is 0, so 2 and 1547 are divisors of 3094)
3094 / 3 = 1031.3333333333 (the remainder is 1, so 3 is not a divisor of 3094)
...
3094 / 54 = 57.296296296296 (the remainder is 16, so 54 is not a divisor of 3094)
3094 / 55 = 56.254545454545 (the remainder is 14, so 55 is not a divisor of 3094)