What are the divisors of 575?

1, 5, 23, 25, 115, 575

There is a total of 6 positive divisors.
The sum of these divisors is 744.
The arithmetic mean is 124.

6 odd divisors

1, 5, 23, 25, 115, 575

How to compute the divisors of 575?

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 575 by each of the numbers from 1 to 575 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)

575 / 1 = 575 (the remainder is 0, so 1 is a divisor of 575)
575 / 2 = 287.5 (the remainder is 1, so 2 is not a divisor of 575)
575 / 3 = 191.66666666667 (the remainder is 2, so 3 is not a divisor of 575)
...
575 / 574 = 1.0017421602787 (the remainder is 1, so 574 is not a divisor of 575)
575 / 575 = 1 (the remainder is 0, so 575 is a divisor of 575)

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 575 (i.e. 23.979157616564). 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 $\frac{N}{d} = D$ )

575 / 1 = 575 (the remainder is 0, so 1 and 575 are divisors of 575)
575 / 2 = 287.5 (the remainder is 1, so 2 is not a divisor of 575)
575 / 3 = 191.66666666667 (the remainder is 2, so 3 is not a divisor of 575)
...
575 / 22 = 26.136363636364 (the remainder is 3, so 22 is not a divisor of 575)
575 / 23 = 25 (the remainder is 0, so 23 and 25 are divisors of 575)