What are the divisors of 4094?

1, 2, 23, 46, 89, 178, 2047, 4094

There is a total of 8 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 810.

4 even divisors

2, 46, 178, 4094

4 odd divisors

1, 23, 89, 2047

How to compute the divisors of 4094?

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 4094 by each of the numbers from 1 to 4094 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)

4094 / 1 = 4094 (the remainder is 0, so 1 is a divisor of 4094)
4094 / 2 = 2047 (the remainder is 0, so 2 is a divisor of 4094)
4094 / 3 = 1364.6666666667 (the remainder is 2, so 3 is not a divisor of 4094)
...
4094 / 4093 = 1.00024431957 (the remainder is 1, so 4093 is not a divisor of 4094)
4094 / 4094 = 1 (the remainder is 0, so 4094 is a divisor of 4094)

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 4094 (i.e. 63.984373092186). 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 $\frac{N}{d} = D$ )

4094 / 1 = 4094 (the remainder is 0, so 1 and 4094 are divisors of 4094)
4094 / 2 = 2047 (the remainder is 0, so 2 and 2047 are divisors of 4094)
4094 / 3 = 1364.6666666667 (the remainder is 2, so 3 is not a divisor of 4094)
...
4094 / 62 = 66.032258064516 (the remainder is 2, so 62 is not a divisor of 4094)
4094 / 63 = 64.984126984127 (the remainder is 62, so 63 is not a divisor of 4094)