What are the divisors of 3226?

1, 2, 1613, 3226

There is a total of 4 positive divisors.
The sum of these divisors is 4842.
The arithmetic mean is 1210.5.

2 even divisors

2, 3226

2 odd divisors

1, 1613

How to compute the divisors of 3226?

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 3226 by each of the numbers from 1 to 3226 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)

3226 / 1 = 3226 (the remainder is 0, so 1 is a divisor of 3226)
3226 / 2 = 1613 (the remainder is 0, so 2 is a divisor of 3226)
3226 / 3 = 1075.3333333333 (the remainder is 1, so 3 is not a divisor of 3226)
...
3226 / 3225 = 1.0003100775194 (the remainder is 1, so 3225 is not a divisor of 3226)
3226 / 3226 = 1 (the remainder is 0, so 3226 is a divisor of 3226)

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 3226 (i.e. 56.797887284652). 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 $\frac{N}{d} = D$ )

3226 / 1 = 3226 (the remainder is 0, so 1 and 3226 are divisors of 3226)
3226 / 2 = 1613 (the remainder is 0, so 2 and 1613 are divisors of 3226)
3226 / 3 = 1075.3333333333 (the remainder is 1, so 3 is not a divisor of 3226)
...
3226 / 55 = 58.654545454545 (the remainder is 36, so 55 is not a divisor of 3226)
3226 / 56 = 57.607142857143 (the remainder is 34, so 56 is not a divisor of 3226)