What are the divisors of 7094?

1, 2, 3547, 7094

There is a total of 4 positive divisors.
The sum of these divisors is 10644.
The arithmetic mean is 2661.

2 even divisors

2, 7094

2 odd divisors

1, 3547

How to compute the divisors of 7094?

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 7094 by each of the numbers from 1 to 7094 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)

7094 / 1 = 7094 (the remainder is 0, so 1 is a divisor of 7094)
7094 / 2 = 3547 (the remainder is 0, so 2 is a divisor of 7094)
7094 / 3 = 2364.6666666667 (the remainder is 2, so 3 is not a divisor of 7094)
...
7094 / 7093 = 1.0001409840688 (the remainder is 1, so 7093 is not a divisor of 7094)
7094 / 7094 = 1 (the remainder is 0, so 7094 is a divisor of 7094)

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 7094 (i.e. 84.225886756982). 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 $\frac{N}{d} = D$ )

7094 / 1 = 7094 (the remainder is 0, so 1 and 7094 are divisors of 7094)
7094 / 2 = 3547 (the remainder is 0, so 2 and 3547 are divisors of 7094)
7094 / 3 = 2364.6666666667 (the remainder is 2, so 3 is not a divisor of 7094)
...
7094 / 83 = 85.469879518072 (the remainder is 39, so 83 is not a divisor of 7094)
7094 / 84 = 84.452380952381 (the remainder is 38, so 84 is not a divisor of 7094)