What are the divisors of 2236?

1, 2, 4, 13, 26, 43, 52, 86, 172, 559, 1118, 2236

There is a total of 12 positive divisors.
The sum of these divisors is 4312.
The arithmetic mean is 359.33333333333.

8 even divisors

2, 4, 26, 52, 86, 172, 1118, 2236

4 odd divisors

1, 13, 43, 559

How to compute the divisors of 2236?

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 2236 by each of the numbers from 1 to 2236 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)

2236 / 1 = 2236 (the remainder is 0, so 1 is a divisor of 2236)
2236 / 2 = 1118 (the remainder is 0, so 2 is a divisor of 2236)
2236 / 3 = 745.33333333333 (the remainder is 1, so 3 is not a divisor of 2236)
...
2236 / 2235 = 1.0004474272931 (the remainder is 1, so 2235 is not a divisor of 2236)
2236 / 2236 = 1 (the remainder is 0, so 2236 is a divisor of 2236)

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 2236 (i.e. 47.286361670148). 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 $\frac{N}{d} = D$ )

2236 / 1 = 2236 (the remainder is 0, so 1 and 2236 are divisors of 2236)
2236 / 2 = 1118 (the remainder is 0, so 2 and 1118 are divisors of 2236)
2236 / 3 = 745.33333333333 (the remainder is 1, so 3 is not a divisor of 2236)
...
2236 / 46 = 48.608695652174 (the remainder is 28, so 46 is not a divisor of 2236)
2236 / 47 = 47.574468085106 (the remainder is 27, so 47 is not a divisor of 2236)