What are the divisors of 2094?

1, 2, 3, 6, 349, 698, 1047, 2094

There is a total of 8 positive divisors.
The sum of these divisors is 4200.
The arithmetic mean is 525.

4 even divisors

2, 6, 698, 2094

4 odd divisors

1, 3, 349, 1047

How to compute the divisors of 2094?

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 2094 by each of the numbers from 1 to 2094 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)

2094 / 1 = 2094 (the remainder is 0, so 1 is a divisor of 2094)
2094 / 2 = 1047 (the remainder is 0, so 2 is a divisor of 2094)
2094 / 3 = 698 (the remainder is 0, so 3 is a divisor of 2094)
...
2094 / 2093 = 1.0004777830865 (the remainder is 1, so 2093 is not a divisor of 2094)
2094 / 2094 = 1 (the remainder is 0, so 2094 is a divisor of 2094)

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 2094 (i.e. 45.76024475459). 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 $\frac{N}{d} = D$ )

2094 / 1 = 2094 (the remainder is 0, so 1 and 2094 are divisors of 2094)
2094 / 2 = 1047 (the remainder is 0, so 2 and 1047 are divisors of 2094)
2094 / 3 = 698 (the remainder is 0, so 3 and 698 are divisors of 2094)
...
2094 / 44 = 47.590909090909 (the remainder is 26, so 44 is not a divisor of 2094)
2094 / 45 = 46.533333333333 (the remainder is 24, so 45 is not a divisor of 2094)