What are the divisors of 2325?

1, 3, 5, 15, 25, 31, 75, 93, 155, 465, 775, 2325

There is a total of 12 positive divisors.
The sum of these divisors is 3968.
The arithmetic mean is 330.66666666667.

12 odd divisors

1, 3, 5, 15, 25, 31, 75, 93, 155, 465, 775, 2325

How to compute the divisors of 2325?

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 2325 by each of the numbers from 1 to 2325 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)

2325 / 1 = 2325 (the remainder is 0, so 1 is a divisor of 2325)
2325 / 2 = 1162.5 (the remainder is 1, so 2 is not a divisor of 2325)
2325 / 3 = 775 (the remainder is 0, so 3 is a divisor of 2325)
...
2325 / 2324 = 1.000430292599 (the remainder is 1, so 2324 is not a divisor of 2325)
2325 / 2325 = 1 (the remainder is 0, so 2325 is a divisor of 2325)

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 2325 (i.e. 48.218253804965). 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 $\frac{N}{d} = D$ )

2325 / 1 = 2325 (the remainder is 0, so 1 and 2325 are divisors of 2325)
2325 / 2 = 1162.5 (the remainder is 1, so 2 is not a divisor of 2325)
2325 / 3 = 775 (the remainder is 0, so 3 and 775 are divisors of 2325)
...
2325 / 47 = 49.468085106383 (the remainder is 22, so 47 is not a divisor of 2325)
2325 / 48 = 48.4375 (the remainder is 21, so 48 is not a divisor of 2325)