What are the divisors of 9105?

1, 3, 5, 15, 607, 1821, 3035, 9105

There is a total of 8 positive divisors.
The sum of these divisors is 14592.
The arithmetic mean is 1824.

8 odd divisors

1, 3, 5, 15, 607, 1821, 3035, 9105

How to compute the divisors of 9105?

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 9105 by each of the numbers from 1 to 9105 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)

9105 / 1 = 9105 (the remainder is 0, so 1 is a divisor of 9105)
9105 / 2 = 4552.5 (the remainder is 1, so 2 is not a divisor of 9105)
9105 / 3 = 3035 (the remainder is 0, so 3 is a divisor of 9105)
...
9105 / 9104 = 1.0001098418278 (the remainder is 1, so 9104 is not a divisor of 9105)
9105 / 9105 = 1 (the remainder is 0, so 9105 is a divisor of 9105)

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 9105 (i.e. 95.420123663722). 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 $\frac{N}{d} = D$ )

9105 / 1 = 9105 (the remainder is 0, so 1 and 9105 are divisors of 9105)
9105 / 2 = 4552.5 (the remainder is 1, so 2 is not a divisor of 9105)
9105 / 3 = 3035 (the remainder is 0, so 3 and 3035 are divisors of 9105)
...
9105 / 94 = 96.86170212766 (the remainder is 81, so 94 is not a divisor of 9105)
9105 / 95 = 95.842105263158 (the remainder is 80, so 95 is not a divisor of 9105)