What are the divisors of 7028?

1, 2, 4, 7, 14, 28, 251, 502, 1004, 1757, 3514, 7028

There is a total of 12 positive divisors.
The sum of these divisors is 14112.
The arithmetic mean is 1176.

8 even divisors

2, 4, 14, 28, 502, 1004, 3514, 7028

4 odd divisors

1, 7, 251, 1757

How to compute the divisors of 7028?

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 7028 by each of the numbers from 1 to 7028 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)

7028 / 1 = 7028 (the remainder is 0, so 1 is a divisor of 7028)
7028 / 2 = 3514 (the remainder is 0, so 2 is a divisor of 7028)
7028 / 3 = 2342.6666666667 (the remainder is 2, so 3 is not a divisor of 7028)
...
7028 / 7027 = 1.0001423082396 (the remainder is 1, so 7027 is not a divisor of 7028)
7028 / 7028 = 1 (the remainder is 0, so 7028 is a divisor of 7028)

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 7028 (i.e. 83.833167660539). 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 $\frac{N}{d} = D$ )

7028 / 1 = 7028 (the remainder is 0, so 1 and 7028 are divisors of 7028)
7028 / 2 = 3514 (the remainder is 0, so 2 and 3514 are divisors of 7028)
7028 / 3 = 2342.6666666667 (the remainder is 2, so 3 is not a divisor of 7028)
...
7028 / 82 = 85.707317073171 (the remainder is 58, so 82 is not a divisor of 7028)
7028 / 83 = 84.674698795181 (the remainder is 56, so 83 is not a divisor of 7028)