What are the divisors of 2136?

1, 2, 3, 4, 6, 8, 12, 24, 89, 178, 267, 356, 534, 712, 1068, 2136

There is a total of 16 positive divisors.
The sum of these divisors is 5400.
The arithmetic mean is 337.5.

12 even divisors

2, 4, 6, 8, 12, 24, 178, 356, 534, 712, 1068, 2136

4 odd divisors

1, 3, 89, 267

How to compute the divisors of 2136?

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 2136 by each of the numbers from 1 to 2136 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)

2136 / 1 = 2136 (the remainder is 0, so 1 is a divisor of 2136)
2136 / 2 = 1068 (the remainder is 0, so 2 is a divisor of 2136)
2136 / 3 = 712 (the remainder is 0, so 3 is a divisor of 2136)
...
2136 / 2135 = 1.0004683840749 (the remainder is 1, so 2135 is not a divisor of 2136)
2136 / 2136 = 1 (the remainder is 0, so 2136 is a divisor of 2136)

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 2136 (i.e. 46.216880033165). 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 $\frac{N}{d} = D$ )

2136 / 1 = 2136 (the remainder is 0, so 1 and 2136 are divisors of 2136)
2136 / 2 = 1068 (the remainder is 0, so 2 and 1068 are divisors of 2136)
2136 / 3 = 712 (the remainder is 0, so 3 and 712 are divisors of 2136)
...
2136 / 45 = 47.466666666667 (the remainder is 21, so 45 is not a divisor of 2136)
2136 / 46 = 46.434782608696 (the remainder is 20, so 46 is not a divisor of 2136)