What are the divisors of 7108?

1, 2, 4, 1777, 3554, 7108

There is a total of 6 positive divisors.
The sum of these divisors is 12446.
The arithmetic mean is 2074.3333333333.

4 even divisors

2, 4, 3554, 7108

2 odd divisors

1, 1777

How to compute the divisors of 7108?

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 7108 by each of the numbers from 1 to 7108 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)

7108 / 1 = 7108 (the remainder is 0, so 1 is a divisor of 7108)
7108 / 2 = 3554 (the remainder is 0, so 2 is a divisor of 7108)
7108 / 3 = 2369.3333333333 (the remainder is 1, so 3 is not a divisor of 7108)
...
7108 / 7107 = 1.0001407063459 (the remainder is 1, so 7107 is not a divisor of 7108)
7108 / 7108 = 1 (the remainder is 0, so 7108 is a divisor of 7108)

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 7108 (i.e. 84.308955633432). 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 $\frac{N}{d} = D$ )

7108 / 1 = 7108 (the remainder is 0, so 1 and 7108 are divisors of 7108)
7108 / 2 = 3554 (the remainder is 0, so 2 and 3554 are divisors of 7108)
7108 / 3 = 2369.3333333333 (the remainder is 1, so 3 is not a divisor of 7108)
...
7108 / 83 = 85.638554216867 (the remainder is 53, so 83 is not a divisor of 7108)
7108 / 84 = 84.619047619048 (the remainder is 52, so 84 is not a divisor of 7108)