What are the divisors of 2175?

1, 3, 5, 15, 25, 29, 75, 87, 145, 435, 725, 2175

There is a total of 12 positive divisors.
The sum of these divisors is 3720.
The arithmetic mean is 310.

12 odd divisors

1, 3, 5, 15, 25, 29, 75, 87, 145, 435, 725, 2175

How to compute the divisors of 2175?

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 2175 by each of the numbers from 1 to 2175 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)

2175 / 1 = 2175 (the remainder is 0, so 1 is a divisor of 2175)
2175 / 2 = 1087.5 (the remainder is 1, so 2 is not a divisor of 2175)
2175 / 3 = 725 (the remainder is 0, so 3 is a divisor of 2175)
...
2175 / 2174 = 1.0004599816007 (the remainder is 1, so 2174 is not a divisor of 2175)
2175 / 2175 = 1 (the remainder is 0, so 2175 is a divisor of 2175)

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 2175 (i.e. 46.636895265444). 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 $\frac{N}{d} = D$ )

2175 / 1 = 2175 (the remainder is 0, so 1 and 2175 are divisors of 2175)
2175 / 2 = 1087.5 (the remainder is 1, so 2 is not a divisor of 2175)
2175 / 3 = 725 (the remainder is 0, so 3 and 725 are divisors of 2175)
...
2175 / 45 = 48.333333333333 (the remainder is 15, so 45 is not a divisor of 2175)
2175 / 46 = 47.282608695652 (the remainder is 13, so 46 is not a divisor of 2175)