What are the divisors of 6094?

1, 2, 11, 22, 277, 554, 3047, 6094

There is a total of 8 positive divisors.
The sum of these divisors is 10008.
The arithmetic mean is 1251.

4 even divisors

2, 22, 554, 6094

4 odd divisors

1, 11, 277, 3047

How to compute the divisors of 6094?

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 6094 by each of the numbers from 1 to 6094 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)

6094 / 1 = 6094 (the remainder is 0, so 1 is a divisor of 6094)
6094 / 2 = 3047 (the remainder is 0, so 2 is a divisor of 6094)
6094 / 3 = 2031.3333333333 (the remainder is 1, so 3 is not a divisor of 6094)
...
6094 / 6093 = 1.0001641227638 (the remainder is 1, so 6093 is not a divisor of 6094)
6094 / 6094 = 1 (the remainder is 0, so 6094 is a divisor of 6094)

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 6094 (i.e. 78.064076245095). 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 $\frac{N}{d} = D$ )

6094 / 1 = 6094 (the remainder is 0, so 1 and 6094 are divisors of 6094)
6094 / 2 = 3047 (the remainder is 0, so 2 and 3047 are divisors of 6094)
6094 / 3 = 2031.3333333333 (the remainder is 1, so 3 is not a divisor of 6094)
...
6094 / 77 = 79.142857142857 (the remainder is 11, so 77 is not a divisor of 6094)
6094 / 78 = 78.128205128205 (the remainder is 10, so 78 is not a divisor of 6094)