What are the divisors of 7027?

1, 7027

There is a total of 2 positive divisors.
The sum of these divisors is 7028.
The arithmetic mean is 3514.

2 odd divisors

1, 7027

How to compute the divisors of 7027?

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 7027 by each of the numbers from 1 to 7027 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)

7027 / 1 = 7027 (the remainder is 0, so 1 is a divisor of 7027)
7027 / 2 = 3513.5 (the remainder is 1, so 2 is not a divisor of 7027)
7027 / 3 = 2342.3333333333 (the remainder is 1, so 3 is not a divisor of 7027)
...
7027 / 7026 = 1.0001423284942 (the remainder is 1, so 7026 is not a divisor of 7027)
7027 / 7027 = 1 (the remainder is 0, so 7027 is a divisor of 7027)

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 7027 (i.e. 83.827203221866). 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 $\frac{N}{d} = D$ )

7027 / 1 = 7027 (the remainder is 0, so 1 and 7027 are divisors of 7027)
7027 / 2 = 3513.5 (the remainder is 1, so 2 is not a divisor of 7027)
7027 / 3 = 2342.3333333333 (the remainder is 1, so 3 is not a divisor of 7027)
...
7027 / 82 = 85.69512195122 (the remainder is 57, so 82 is not a divisor of 7027)
7027 / 83 = 84.66265060241 (the remainder is 55, so 83 is not a divisor of 7027)