What are the divisors of 7103?

1, 7103

There is a total of 2 positive divisors.
The sum of these divisors is 7104.
The arithmetic mean is 3552.

2 odd divisors

1, 7103

How to compute the divisors of 7103?

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 7103 by each of the numbers from 1 to 7103 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)

7103 / 1 = 7103 (the remainder is 0, so 1 is a divisor of 7103)
7103 / 2 = 3551.5 (the remainder is 1, so 2 is not a divisor of 7103)
7103 / 3 = 2367.6666666667 (the remainder is 2, so 3 is not a divisor of 7103)
...
7103 / 7102 = 1.0001408054069 (the remainder is 1, so 7102 is not a divisor of 7103)
7103 / 7103 = 1 (the remainder is 0, so 7103 is a divisor of 7103)

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 7103 (i.e. 84.27929757657). 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 $\frac{N}{d} = D$ )

7103 / 1 = 7103 (the remainder is 0, so 1 and 7103 are divisors of 7103)
7103 / 2 = 3551.5 (the remainder is 1, so 2 is not a divisor of 7103)
7103 / 3 = 2367.6666666667 (the remainder is 2, so 3 is not a divisor of 7103)
...
7103 / 83 = 85.578313253012 (the remainder is 48, so 83 is not a divisor of 7103)
7103 / 84 = 84.559523809524 (the remainder is 47, so 84 is not a divisor of 7103)