What are the divisors of 3075?

1, 3, 5, 15, 25, 41, 75, 123, 205, 615, 1025, 3075

There is a total of 12 positive divisors.
The sum of these divisors is 5208.
The arithmetic mean is 434.

12 odd divisors

1, 3, 5, 15, 25, 41, 75, 123, 205, 615, 1025, 3075

How to compute the divisors of 3075?

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 3075 by each of the numbers from 1 to 3075 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)

3075 / 1 = 3075 (the remainder is 0, so 1 is a divisor of 3075)
3075 / 2 = 1537.5 (the remainder is 1, so 2 is not a divisor of 3075)
3075 / 3 = 1025 (the remainder is 0, so 3 is a divisor of 3075)
...
3075 / 3074 = 1.0003253090436 (the remainder is 1, so 3074 is not a divisor of 3075)
3075 / 3075 = 1 (the remainder is 0, so 3075 is a divisor of 3075)

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 3075 (i.e. 55.452682532047). 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 $\frac{N}{d} = D$ )

3075 / 1 = 3075 (the remainder is 0, so 1 and 3075 are divisors of 3075)
3075 / 2 = 1537.5 (the remainder is 1, so 2 is not a divisor of 3075)
3075 / 3 = 1025 (the remainder is 0, so 3 and 1025 are divisors of 3075)
...
3075 / 54 = 56.944444444444 (the remainder is 51, so 54 is not a divisor of 3075)
3075 / 55 = 55.909090909091 (the remainder is 50, so 55 is not a divisor of 3075)