What are the divisors of 2575?

1, 5, 25, 103, 515, 2575

There is a total of 6 positive divisors.
The sum of these divisors is 3224.
The arithmetic mean is 537.33333333333.

6 odd divisors

1, 5, 25, 103, 515, 2575

How to compute the divisors of 2575?

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 2575 by each of the numbers from 1 to 2575 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)

2575 / 1 = 2575 (the remainder is 0, so 1 is a divisor of 2575)
2575 / 2 = 1287.5 (the remainder is 1, so 2 is not a divisor of 2575)
2575 / 3 = 858.33333333333 (the remainder is 1, so 3 is not a divisor of 2575)
...
2575 / 2574 = 1.0003885003885 (the remainder is 1, so 2574 is not a divisor of 2575)
2575 / 2575 = 1 (the remainder is 0, so 2575 is a divisor of 2575)

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 2575 (i.e. 50.744457825461). 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 $\frac{N}{d} = D$ )

2575 / 1 = 2575 (the remainder is 0, so 1 and 2575 are divisors of 2575)
2575 / 2 = 1287.5 (the remainder is 1, so 2 is not a divisor of 2575)
2575 / 3 = 858.33333333333 (the remainder is 1, so 3 is not a divisor of 2575)
...
2575 / 49 = 52.551020408163 (the remainder is 27, so 49 is not a divisor of 2575)
2575 / 50 = 51.5 (the remainder is 25, so 50 is not a divisor of 2575)