What are the divisors of 2217?

1, 3, 739, 2217

There is a total of 4 positive divisors.
The sum of these divisors is 2960.
The arithmetic mean is 740.

4 odd divisors

1, 3, 739, 2217

How to compute the divisors of 2217?

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 2217 by each of the numbers from 1 to 2217 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)

2217 / 1 = 2217 (the remainder is 0, so 1 is a divisor of 2217)
2217 / 2 = 1108.5 (the remainder is 1, so 2 is not a divisor of 2217)
2217 / 3 = 739 (the remainder is 0, so 3 is a divisor of 2217)
...
2217 / 2216 = 1.0004512635379 (the remainder is 1, so 2216 is not a divisor of 2217)
2217 / 2217 = 1 (the remainder is 0, so 2217 is a divisor of 2217)

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 2217 (i.e. 47.085029467974). 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 $\frac{N}{d} = D$ )

2217 / 1 = 2217 (the remainder is 0, so 1 and 2217 are divisors of 2217)
2217 / 2 = 1108.5 (the remainder is 1, so 2 is not a divisor of 2217)
2217 / 3 = 739 (the remainder is 0, so 3 and 739 are divisors of 2217)
...
2217 / 46 = 48.195652173913 (the remainder is 9, so 46 is not a divisor of 2217)
2217 / 47 = 47.170212765957 (the remainder is 8, so 47 is not a divisor of 2217)