What are the divisors of 2075?

1, 5, 25, 83, 415, 2075

There is a total of 6 positive divisors.
The sum of these divisors is 2604.
The arithmetic mean is 434.

6 odd divisors

1, 5, 25, 83, 415, 2075

How to compute the divisors of 2075?

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 2075 by each of the numbers from 1 to 2075 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)

2075 / 1 = 2075 (the remainder is 0, so 1 is a divisor of 2075)
2075 / 2 = 1037.5 (the remainder is 1, so 2 is not a divisor of 2075)
2075 / 3 = 691.66666666667 (the remainder is 2, so 3 is not a divisor of 2075)
...
2075 / 2074 = 1.0004821600771 (the remainder is 1, so 2074 is not a divisor of 2075)
2075 / 2075 = 1 (the remainder is 0, so 2075 is a divisor of 2075)

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 2075 (i.e. 45.552167895721). 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 $\frac{N}{d} = D$ )

2075 / 1 = 2075 (the remainder is 0, so 1 and 2075 are divisors of 2075)
2075 / 2 = 1037.5 (the remainder is 1, so 2 is not a divisor of 2075)
2075 / 3 = 691.66666666667 (the remainder is 2, so 3 is not a divisor of 2075)
...
2075 / 44 = 47.159090909091 (the remainder is 7, so 44 is not a divisor of 2075)
2075 / 45 = 46.111111111111 (the remainder is 5, so 45 is not a divisor of 2075)