What are the divisors of 7036?

1, 2, 4, 1759, 3518, 7036

There is a total of 6 positive divisors.
The sum of these divisors is 12320.
The arithmetic mean is 2053.3333333333.

4 even divisors

2, 4, 3518, 7036

2 odd divisors

1, 1759

How to compute the divisors of 7036?

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 7036 by each of the numbers from 1 to 7036 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)

7036 / 1 = 7036 (the remainder is 0, so 1 is a divisor of 7036)
7036 / 2 = 3518 (the remainder is 0, so 2 is a divisor of 7036)
7036 / 3 = 2345.3333333333 (the remainder is 1, so 3 is not a divisor of 7036)
...
7036 / 7035 = 1.0001421464108 (the remainder is 1, so 7035 is not a divisor of 7036)
7036 / 7036 = 1 (the remainder is 0, so 7036 is a divisor of 7036)

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 7036 (i.e. 83.880867902043). 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 $\frac{N}{d} = D$ )

7036 / 1 = 7036 (the remainder is 0, so 1 and 7036 are divisors of 7036)
7036 / 2 = 3518 (the remainder is 0, so 2 and 3518 are divisors of 7036)
7036 / 3 = 2345.3333333333 (the remainder is 1, so 3 is not a divisor of 7036)
...
7036 / 82 = 85.80487804878 (the remainder is 66, so 82 is not a divisor of 7036)
7036 / 83 = 84.771084337349 (the remainder is 64, so 83 is not a divisor of 7036)