What are the divisors of 2150?

1, 2, 5, 10, 25, 43, 50, 86, 215, 430, 1075, 2150

There is a total of 12 positive divisors.
The sum of these divisors is 4092.
The arithmetic mean is 341.

6 even divisors

2, 10, 50, 86, 430, 2150

6 odd divisors

1, 5, 25, 43, 215, 1075

How to compute the divisors of 2150?

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 2150 by each of the numbers from 1 to 2150 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)

2150 / 1 = 2150 (the remainder is 0, so 1 is a divisor of 2150)
2150 / 2 = 1075 (the remainder is 0, so 2 is a divisor of 2150)
2150 / 3 = 716.66666666667 (the remainder is 2, so 3 is not a divisor of 2150)
...
2150 / 2149 = 1.0004653327129 (the remainder is 1, so 2149 is not a divisor of 2150)
2150 / 2150 = 1 (the remainder is 0, so 2150 is a divisor of 2150)

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 2150 (i.e. 46.368092477479). 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 $\frac{N}{d} = D$ )

2150 / 1 = 2150 (the remainder is 0, so 1 and 2150 are divisors of 2150)
2150 / 2 = 1075 (the remainder is 0, so 2 and 1075 are divisors of 2150)
2150 / 3 = 716.66666666667 (the remainder is 2, so 3 is not a divisor of 2150)
...
2150 / 45 = 47.777777777778 (the remainder is 35, so 45 is not a divisor of 2150)
2150 / 46 = 46.739130434783 (the remainder is 34, so 46 is not a divisor of 2150)