What are the divisors of 4575?

1, 3, 5, 15, 25, 61, 75, 183, 305, 915, 1525, 4575

There is a total of 12 positive divisors.
The sum of these divisors is 7688.
The arithmetic mean is 640.66666666667.

12 odd divisors

1, 3, 5, 15, 25, 61, 75, 183, 305, 915, 1525, 4575

How to compute the divisors of 4575?

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 4575 by each of the numbers from 1 to 4575 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)

4575 / 1 = 4575 (the remainder is 0, so 1 is a divisor of 4575)
4575 / 2 = 2287.5 (the remainder is 1, so 2 is not a divisor of 4575)
4575 / 3 = 1525 (the remainder is 0, so 3 is a divisor of 4575)
...
4575 / 4574 = 1.0002186270223 (the remainder is 1, so 4574 is not a divisor of 4575)
4575 / 4575 = 1 (the remainder is 0, so 4575 is a divisor of 4575)

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 4575 (i.e. 67.638746292343). 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 $\frac{N}{d} = D$ )

4575 / 1 = 4575 (the remainder is 0, so 1 and 4575 are divisors of 4575)
4575 / 2 = 2287.5 (the remainder is 1, so 2 is not a divisor of 4575)
4575 / 3 = 1525 (the remainder is 0, so 3 and 1525 are divisors of 4575)
...
4575 / 66 = 69.318181818182 (the remainder is 21, so 66 is not a divisor of 4575)
4575 / 67 = 68.283582089552 (the remainder is 19, so 67 is not a divisor of 4575)