What are the divisors of 2715?

1, 3, 5, 15, 181, 543, 905, 2715

There is a total of 8 positive divisors.
The sum of these divisors is 4368.
The arithmetic mean is 546.

8 odd divisors

1, 3, 5, 15, 181, 543, 905, 2715

How to compute the divisors of 2715?

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 2715 by each of the numbers from 1 to 2715 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)

2715 / 1 = 2715 (the remainder is 0, so 1 is a divisor of 2715)
2715 / 2 = 1357.5 (the remainder is 1, so 2 is not a divisor of 2715)
2715 / 3 = 905 (the remainder is 0, so 3 is a divisor of 2715)
...
2715 / 2714 = 1.0003684598379 (the remainder is 1, so 2714 is not a divisor of 2715)
2715 / 2715 = 1 (the remainder is 0, so 2715 is a divisor of 2715)

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 2715 (i.e. 52.105661880452). 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 $\frac{N}{d} = D$ )

2715 / 1 = 2715 (the remainder is 0, so 1 and 2715 are divisors of 2715)
2715 / 2 = 1357.5 (the remainder is 1, so 2 is not a divisor of 2715)
2715 / 3 = 905 (the remainder is 0, so 3 and 905 are divisors of 2715)
...
2715 / 51 = 53.235294117647 (the remainder is 12, so 51 is not a divisor of 2715)
2715 / 52 = 52.211538461538 (the remainder is 11, so 52 is not a divisor of 2715)