What are the divisors of 2104?

1, 2, 4, 8, 263, 526, 1052, 2104

There is a total of 8 positive divisors.
The sum of these divisors is 3960.
The arithmetic mean is 495.

6 even divisors

2, 4, 8, 526, 1052, 2104

2 odd divisors

1, 263

How to compute the divisors of 2104?

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 2104 by each of the numbers from 1 to 2104 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)

2104 / 1 = 2104 (the remainder is 0, so 1 is a divisor of 2104)
2104 / 2 = 1052 (the remainder is 0, so 2 is a divisor of 2104)
2104 / 3 = 701.33333333333 (the remainder is 1, so 3 is not a divisor of 2104)
...
2104 / 2103 = 1.0004755111745 (the remainder is 1, so 2103 is not a divisor of 2104)
2104 / 2104 = 1 (the remainder is 0, so 2104 is a divisor of 2104)

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 2104 (i.e. 45.869379764719). 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 $\frac{N}{d} = D$ )

2104 / 1 = 2104 (the remainder is 0, so 1 and 2104 are divisors of 2104)
2104 / 2 = 1052 (the remainder is 0, so 2 and 1052 are divisors of 2104)
2104 / 3 = 701.33333333333 (the remainder is 1, so 3 is not a divisor of 2104)
...
2104 / 44 = 47.818181818182 (the remainder is 36, so 44 is not a divisor of 2104)
2104 / 45 = 46.755555555556 (the remainder is 34, so 45 is not a divisor of 2104)