What are the divisors of 7039?

1, 7039

There is a total of 2 positive divisors.
The sum of these divisors is 7040.
The arithmetic mean is 3520.

2 odd divisors

1, 7039

How to compute the divisors of 7039?

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 7039 by each of the numbers from 1 to 7039 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)

7039 / 1 = 7039 (the remainder is 0, so 1 is a divisor of 7039)
7039 / 2 = 3519.5 (the remainder is 1, so 2 is not a divisor of 7039)
7039 / 3 = 2346.3333333333 (the remainder is 1, so 3 is not a divisor of 7039)
...
7039 / 7038 = 1.0001420858198 (the remainder is 1, so 7038 is not a divisor of 7039)
7039 / 7039 = 1 (the remainder is 0, so 7039 is a divisor of 7039)

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 7039 (i.e. 83.898748500797). 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 $\frac{N}{d} = D$ )

7039 / 1 = 7039 (the remainder is 0, so 1 and 7039 are divisors of 7039)
7039 / 2 = 3519.5 (the remainder is 1, so 2 is not a divisor of 7039)
7039 / 3 = 2346.3333333333 (the remainder is 1, so 3 is not a divisor of 7039)
...
7039 / 82 = 85.841463414634 (the remainder is 69, so 82 is not a divisor of 7039)
7039 / 83 = 84.807228915663 (the remainder is 67, so 83 is not a divisor of 7039)