What are the divisors of 2107?

1, 7, 43, 49, 301, 2107

There is a total of 6 positive divisors.
The sum of these divisors is 2508.
The arithmetic mean is 418.

6 odd divisors

1, 7, 43, 49, 301, 2107

How to compute the divisors of 2107?

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 2107 by each of the numbers from 1 to 2107 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)

2107 / 1 = 2107 (the remainder is 0, so 1 is a divisor of 2107)
2107 / 2 = 1053.5 (the remainder is 1, so 2 is not a divisor of 2107)
2107 / 3 = 702.33333333333 (the remainder is 1, so 3 is not a divisor of 2107)
...
2107 / 2106 = 1.0004748338082 (the remainder is 1, so 2106 is not a divisor of 2107)
2107 / 2107 = 1 (the remainder is 0, so 2107 is a divisor of 2107)

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 2107 (i.e. 45.902069670114). 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 $\frac{N}{d} = D$ )

2107 / 1 = 2107 (the remainder is 0, so 1 and 2107 are divisors of 2107)
2107 / 2 = 1053.5 (the remainder is 1, so 2 is not a divisor of 2107)
2107 / 3 = 702.33333333333 (the remainder is 1, so 3 is not a divisor of 2107)
...
2107 / 44 = 47.886363636364 (the remainder is 39, so 44 is not a divisor of 2107)
2107 / 45 = 46.822222222222 (the remainder is 37, so 45 is not a divisor of 2107)