What are the divisors of 1036?

1, 2, 4, 7, 14, 28, 37, 74, 148, 259, 518, 1036

There is a total of 12 positive divisors.
The sum of these divisors is 2128.
The arithmetic mean is 177.33333333333.

8 even divisors

2, 4, 14, 28, 74, 148, 518, 1036

4 odd divisors

1, 7, 37, 259

How to compute the divisors of 1036?

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 1036 by each of the numbers from 1 to 1036 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)

1036 / 1 = 1036 (the remainder is 0, so 1 is a divisor of 1036)
1036 / 2 = 518 (the remainder is 0, so 2 is a divisor of 1036)
1036 / 3 = 345.33333333333 (the remainder is 1, so 3 is not a divisor of 1036)
...
1036 / 1035 = 1.0009661835749 (the remainder is 1, so 1035 is not a divisor of 1036)
1036 / 1036 = 1 (the remainder is 0, so 1036 is a divisor of 1036)

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 1036 (i.e. 32.186953878862). 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 $\frac{N}{d} = D$ )

1036 / 1 = 1036 (the remainder is 0, so 1 and 1036 are divisors of 1036)
1036 / 2 = 518 (the remainder is 0, so 2 and 518 are divisors of 1036)
1036 / 3 = 345.33333333333 (the remainder is 1, so 3 is not a divisor of 1036)
...
1036 / 31 = 33.41935483871 (the remainder is 13, so 31 is not a divisor of 1036)
1036 / 32 = 32.375 (the remainder is 12, so 32 is not a divisor of 1036)