What are the divisors of 7023?

1, 3, 2341, 7023

There is a total of 4 positive divisors.
The sum of these divisors is 9368.
The arithmetic mean is 2342.

4 odd divisors

1, 3, 2341, 7023

How to compute the divisors of 7023?

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 7023 by each of the numbers from 1 to 7023 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)

7023 / 1 = 7023 (the remainder is 0, so 1 is a divisor of 7023)
7023 / 2 = 3511.5 (the remainder is 1, so 2 is not a divisor of 7023)
7023 / 3 = 2341 (the remainder is 0, so 3 is a divisor of 7023)
...
7023 / 7022 = 1.0001424095699 (the remainder is 1, so 7022 is not a divisor of 7023)
7023 / 7023 = 1 (the remainder is 0, so 7023 is a divisor of 7023)

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 7023 (i.e. 83.803341222173). 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 $\frac{N}{d} = D$ )

7023 / 1 = 7023 (the remainder is 0, so 1 and 7023 are divisors of 7023)
7023 / 2 = 3511.5 (the remainder is 1, so 2 is not a divisor of 7023)
7023 / 3 = 2341 (the remainder is 0, so 3 and 2341 are divisors of 7023)
...
7023 / 82 = 85.646341463415 (the remainder is 53, so 82 is not a divisor of 7023)
7023 / 83 = 84.614457831325 (the remainder is 51, so 83 is not a divisor of 7023)