What are the divisors of 3218?

1, 2, 1609, 3218

There is a total of 4 positive divisors.
The sum of these divisors is 4830.
The arithmetic mean is 1207.5.

2 even divisors

2, 3218

2 odd divisors

1, 1609

How to compute the divisors of 3218?

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 3218 by each of the numbers from 1 to 3218 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)

3218 / 1 = 3218 (the remainder is 0, so 1 is a divisor of 3218)
3218 / 2 = 1609 (the remainder is 0, so 2 is a divisor of 3218)
3218 / 3 = 1072.6666666667 (the remainder is 2, so 3 is not a divisor of 3218)
...
3218 / 3217 = 1.0003108486167 (the remainder is 1, so 3217 is not a divisor of 3218)
3218 / 3218 = 1 (the remainder is 0, so 3218 is a divisor of 3218)

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 3218 (i.e. 56.727418414731). 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 $\frac{N}{d} = D$ )

3218 / 1 = 3218 (the remainder is 0, so 1 and 3218 are divisors of 3218)
3218 / 2 = 1609 (the remainder is 0, so 2 and 1609 are divisors of 3218)
3218 / 3 = 1072.6666666667 (the remainder is 2, so 3 is not a divisor of 3218)
...
3218 / 55 = 58.509090909091 (the remainder is 28, so 55 is not a divisor of 3218)
3218 / 56 = 57.464285714286 (the remainder is 26, so 56 is not a divisor of 3218)