What are the divisors of 2096?

1, 2, 4, 8, 16, 131, 262, 524, 1048, 2096

There is a total of 10 positive divisors.
The sum of these divisors is 4092.
The arithmetic mean is 409.2.

8 even divisors

2, 4, 8, 16, 262, 524, 1048, 2096

2 odd divisors

1, 131

How to compute the divisors of 2096?

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 2096 by each of the numbers from 1 to 2096 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)

2096 / 1 = 2096 (the remainder is 0, so 1 is a divisor of 2096)
2096 / 2 = 1048 (the remainder is 0, so 2 is a divisor of 2096)
2096 / 3 = 698.66666666667 (the remainder is 2, so 3 is not a divisor of 2096)
...
2096 / 2095 = 1.000477326969 (the remainder is 1, so 2095 is not a divisor of 2096)
2096 / 2096 = 1 (the remainder is 0, so 2096 is a divisor of 2096)

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 2096 (i.e. 45.782092569038). 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 $\frac{N}{d} = D$ )

2096 / 1 = 2096 (the remainder is 0, so 1 and 2096 are divisors of 2096)
2096 / 2 = 1048 (the remainder is 0, so 2 and 1048 are divisors of 2096)
2096 / 3 = 698.66666666667 (the remainder is 2, so 3 is not a divisor of 2096)
...
2096 / 44 = 47.636363636364 (the remainder is 28, so 44 is not a divisor of 2096)
2096 / 45 = 46.577777777778 (the remainder is 26, so 45 is not a divisor of 2096)