What are the divisors of 2050?

1, 2, 5, 10, 25, 41, 50, 82, 205, 410, 1025, 2050

There is a total of 12 positive divisors.
The sum of these divisors is 3906.
The arithmetic mean is 325.5.

6 even divisors

2, 10, 50, 82, 410, 2050

6 odd divisors

1, 5, 25, 41, 205, 1025

How to compute the divisors of 2050?

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 2050 by each of the numbers from 1 to 2050 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)

2050 / 1 = 2050 (the remainder is 0, so 1 is a divisor of 2050)
2050 / 2 = 1025 (the remainder is 0, so 2 is a divisor of 2050)
2050 / 3 = 683.33333333333 (the remainder is 1, so 3 is not a divisor of 2050)
...
2050 / 2049 = 1.0004880429478 (the remainder is 1, so 2049 is not a divisor of 2050)
2050 / 2050 = 1 (the remainder is 0, so 2050 is a divisor of 2050)

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 2050 (i.e. 45.276925690687). 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 $\frac{N}{d} = D$ )

2050 / 1 = 2050 (the remainder is 0, so 1 and 2050 are divisors of 2050)
2050 / 2 = 1025 (the remainder is 0, so 2 and 1025 are divisors of 2050)
2050 / 3 = 683.33333333333 (the remainder is 1, so 3 is not a divisor of 2050)
...
2050 / 44 = 46.590909090909 (the remainder is 26, so 44 is not a divisor of 2050)
2050 / 45 = 45.555555555556 (the remainder is 25, so 45 is not a divisor of 2050)