What are the divisors of 2125?

1, 5, 17, 25, 85, 125, 425, 2125

There is a total of 8 positive divisors.
The sum of these divisors is 2808.
The arithmetic mean is 351.

8 odd divisors

1, 5, 17, 25, 85, 125, 425, 2125

How to compute the divisors of 2125?

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 2125 by each of the numbers from 1 to 2125 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)

2125 / 1 = 2125 (the remainder is 0, so 1 is a divisor of 2125)
2125 / 2 = 1062.5 (the remainder is 1, so 2 is not a divisor of 2125)
2125 / 3 = 708.33333333333 (the remainder is 1, so 3 is not a divisor of 2125)
...
2125 / 2124 = 1.0004708097928 (the remainder is 1, so 2124 is not a divisor of 2125)
2125 / 2125 = 1 (the remainder is 0, so 2125 is a divisor of 2125)

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 2125 (i.e. 46.097722286464). 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 $\frac{N}{d} = D$ )

2125 / 1 = 2125 (the remainder is 0, so 1 and 2125 are divisors of 2125)
2125 / 2 = 1062.5 (the remainder is 1, so 2 is not a divisor of 2125)
2125 / 3 = 708.33333333333 (the remainder is 1, so 3 is not a divisor of 2125)
...
2125 / 45 = 47.222222222222 (the remainder is 10, so 45 is not a divisor of 2125)
2125 / 46 = 46.195652173913 (the remainder is 9, so 46 is not a divisor of 2125)