What are the divisors of 2116?

1, 2, 4, 23, 46, 92, 529, 1058, 2116

There is a total of 9 positive divisors.
The sum of these divisors is 3871.
The arithmetic mean is 430.11111111111.

6 even divisors

2, 4, 46, 92, 1058, 2116

3 odd divisors

1, 23, 529

How to compute the divisors of 2116?

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 2116 by each of the numbers from 1 to 2116 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)

2116 / 1 = 2116 (the remainder is 0, so 1 is a divisor of 2116)
2116 / 2 = 1058 (the remainder is 0, so 2 is a divisor of 2116)
2116 / 3 = 705.33333333333 (the remainder is 1, so 3 is not a divisor of 2116)
...
2116 / 2115 = 1.0004728132388 (the remainder is 1, so 2115 is not a divisor of 2116)
2116 / 2116 = 1 (the remainder is 0, so 2116 is a divisor of 2116)

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 2116 (i.e. 46). 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 $\frac{N}{d} = D$ )

2116 / 1 = 2116 (the remainder is 0, so 1 and 2116 are divisors of 2116)
2116 / 2 = 1058 (the remainder is 0, so 2 and 1058 are divisors of 2116)
2116 / 3 = 705.33333333333 (the remainder is 1, so 3 is not a divisor of 2116)
...
2116 / 45 = 47.022222222222 (the remainder is 1, so 45 is not a divisor of 2116)
2116 / 46 = 46 (the remainder is 0, so 46 and 46 are divisors of 2116)