What are the divisors of 7041?

1, 3, 2347, 7041

There is a total of 4 positive divisors.
The sum of these divisors is 9392.
The arithmetic mean is 2348.

4 odd divisors

1, 3, 2347, 7041

How to compute the divisors of 7041?

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 7041 by each of the numbers from 1 to 7041 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)

7041 / 1 = 7041 (the remainder is 0, so 1 is a divisor of 7041)
7041 / 2 = 3520.5 (the remainder is 1, so 2 is not a divisor of 7041)
7041 / 3 = 2347 (the remainder is 0, so 3 is a divisor of 7041)
...
7041 / 7040 = 1.0001420454545 (the remainder is 1, so 7040 is not a divisor of 7041)
7041 / 7041 = 1 (the remainder is 0, so 7041 is a divisor of 7041)

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 7041 (i.e. 83.910666783193). 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 $\frac{N}{d} = D$ )

7041 / 1 = 7041 (the remainder is 0, so 1 and 7041 are divisors of 7041)
7041 / 2 = 3520.5 (the remainder is 1, so 2 is not a divisor of 7041)
7041 / 3 = 2347 (the remainder is 0, so 3 and 2347 are divisors of 7041)
...
7041 / 82 = 85.865853658537 (the remainder is 71, so 82 is not a divisor of 7041)
7041 / 83 = 84.831325301205 (the remainder is 69, so 83 is not a divisor of 7041)