What are the divisors of 7031?

1, 79, 89, 7031

There is a total of 4 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 1800.

4 odd divisors

1, 79, 89, 7031

How to compute the divisors of 7031?

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 7031 by each of the numbers from 1 to 7031 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)

7031 / 1 = 7031 (the remainder is 0, so 1 is a divisor of 7031)
7031 / 2 = 3515.5 (the remainder is 1, so 2 is not a divisor of 7031)
7031 / 3 = 2343.6666666667 (the remainder is 2, so 3 is not a divisor of 7031)
...
7031 / 7030 = 1.0001422475107 (the remainder is 1, so 7030 is not a divisor of 7031)
7031 / 7031 = 1 (the remainder is 0, so 7031 is a divisor of 7031)

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 7031 (i.e. 83.851058431006). 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 $\frac{N}{d} = D$ )

7031 / 1 = 7031 (the remainder is 0, so 1 and 7031 are divisors of 7031)
7031 / 2 = 3515.5 (the remainder is 1, so 2 is not a divisor of 7031)
7031 / 3 = 2343.6666666667 (the remainder is 2, so 3 is not a divisor of 7031)
...
7031 / 82 = 85.743902439024 (the remainder is 61, so 82 is not a divisor of 7031)
7031 / 83 = 84.710843373494 (the remainder is 59, so 83 is not a divisor of 7031)