What are the divisors of 2156?

1, 2, 4, 7, 11, 14, 22, 28, 44, 49, 77, 98, 154, 196, 308, 539, 1078, 2156

There is a total of 18 positive divisors.
The sum of these divisors is 4788.
The arithmetic mean is 266.

12 even divisors

2, 4, 14, 22, 28, 44, 98, 154, 196, 308, 1078, 2156

6 odd divisors

1, 7, 11, 49, 77, 539

How to compute the divisors of 2156?

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 2156 by each of the numbers from 1 to 2156 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)

2156 / 1 = 2156 (the remainder is 0, so 1 is a divisor of 2156)
2156 / 2 = 1078 (the remainder is 0, so 2 is a divisor of 2156)
2156 / 3 = 718.66666666667 (the remainder is 2, so 3 is not a divisor of 2156)
...
2156 / 2155 = 1.000464037123 (the remainder is 1, so 2155 is not a divisor of 2156)
2156 / 2156 = 1 (the remainder is 0, so 2156 is a divisor of 2156)

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 2156 (i.e. 46.432747064976). 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 $\frac{N}{d} = D$ )

2156 / 1 = 2156 (the remainder is 0, so 1 and 2156 are divisors of 2156)
2156 / 2 = 1078 (the remainder is 0, so 2 and 1078 are divisors of 2156)
2156 / 3 = 718.66666666667 (the remainder is 2, so 3 is not a divisor of 2156)
...
2156 / 45 = 47.911111111111 (the remainder is 41, so 45 is not a divisor of 2156)
2156 / 46 = 46.869565217391 (the remainder is 40, so 46 is not a divisor of 2156)