What are the divisors of 7043?

1, 7043

There is a total of 2 positive divisors.
The sum of these divisors is 7044.
The arithmetic mean is 3522.

2 odd divisors

1, 7043

How to compute the divisors of 7043?

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 7043 by each of the numbers from 1 to 7043 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)

7043 / 1 = 7043 (the remainder is 0, so 1 is a divisor of 7043)
7043 / 2 = 3521.5 (the remainder is 1, so 2 is not a divisor of 7043)
7043 / 3 = 2347.6666666667 (the remainder is 2, so 3 is not a divisor of 7043)
...
7043 / 7042 = 1.0001420051122 (the remainder is 1, so 7042 is not a divisor of 7043)
7043 / 7043 = 1 (the remainder is 0, so 7043 is a divisor of 7043)

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 7043 (i.e. 83.922583373011). 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 $\frac{N}{d} = D$ )

7043 / 1 = 7043 (the remainder is 0, so 1 and 7043 are divisors of 7043)
7043 / 2 = 3521.5 (the remainder is 1, so 2 is not a divisor of 7043)
7043 / 3 = 2347.6666666667 (the remainder is 2, so 3 is not a divisor of 7043)
...
7043 / 82 = 85.890243902439 (the remainder is 73, so 82 is not a divisor of 7043)
7043 / 83 = 84.855421686747 (the remainder is 71, so 83 is not a divisor of 7043)