What are the divisors of 2115?

1, 3, 5, 9, 15, 45, 47, 141, 235, 423, 705, 2115

There is a total of 12 positive divisors.
The sum of these divisors is 3744.
The arithmetic mean is 312.

12 odd divisors

1, 3, 5, 9, 15, 45, 47, 141, 235, 423, 705, 2115

How to compute the divisors of 2115?

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 2115 by each of the numbers from 1 to 2115 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)

2115 / 1 = 2115 (the remainder is 0, so 1 is a divisor of 2115)
2115 / 2 = 1057.5 (the remainder is 1, so 2 is not a divisor of 2115)
2115 / 3 = 705 (the remainder is 0, so 3 is a divisor of 2115)
...
2115 / 2114 = 1.0004730368969 (the remainder is 1, so 2114 is not a divisor of 2115)
2115 / 2115 = 1 (the remainder is 0, so 2115 is a divisor of 2115)

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 2115 (i.e. 45.989129150268). 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 $\frac{N}{d} = D$ )

2115 / 1 = 2115 (the remainder is 0, so 1 and 2115 are divisors of 2115)
2115 / 2 = 1057.5 (the remainder is 1, so 2 is not a divisor of 2115)
2115 / 3 = 705 (the remainder is 0, so 3 and 705 are divisors of 2115)
...
2115 / 44 = 48.068181818182 (the remainder is 3, so 44 is not a divisor of 2115)
2115 / 45 = 47 (the remainder is 0, so 45 and 47 are divisors of 2115)