What are the divisors of 2215?

1, 5, 443, 2215

There is a total of 4 positive divisors.
The sum of these divisors is 2664.
The arithmetic mean is 666.

4 odd divisors

1, 5, 443, 2215

How to compute the divisors of 2215?

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 2215 by each of the numbers from 1 to 2215 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)

2215 / 1 = 2215 (the remainder is 0, so 1 is a divisor of 2215)
2215 / 2 = 1107.5 (the remainder is 1, so 2 is not a divisor of 2215)
2215 / 3 = 738.33333333333 (the remainder is 1, so 3 is not a divisor of 2215)
...
2215 / 2214 = 1.0004516711834 (the remainder is 1, so 2214 is not a divisor of 2215)
2215 / 2215 = 1 (the remainder is 0, so 2215 is a divisor of 2215)

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 2215 (i.e. 47.063786503). 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 $\frac{N}{d} = D$ )

2215 / 1 = 2215 (the remainder is 0, so 1 and 2215 are divisors of 2215)
2215 / 2 = 1107.5 (the remainder is 1, so 2 is not a divisor of 2215)
2215 / 3 = 738.33333333333 (the remainder is 1, so 3 is not a divisor of 2215)
...
2215 / 46 = 48.152173913043 (the remainder is 7, so 46 is not a divisor of 2215)
2215 / 47 = 47.127659574468 (the remainder is 6, so 47 is not a divisor of 2215)