What are the divisors of 3208?

1, 2, 4, 8, 401, 802, 1604, 3208

There is a total of 8 positive divisors.
The sum of these divisors is 6030.
The arithmetic mean is 753.75.

6 even divisors

2, 4, 8, 802, 1604, 3208

2 odd divisors

1, 401

How to compute the divisors of 3208?

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 3208 by each of the numbers from 1 to 3208 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)

3208 / 1 = 3208 (the remainder is 0, so 1 is a divisor of 3208)
3208 / 2 = 1604 (the remainder is 0, so 2 is a divisor of 3208)
3208 / 3 = 1069.3333333333 (the remainder is 1, so 3 is not a divisor of 3208)
...
3208 / 3207 = 1.0003118178983 (the remainder is 1, so 3207 is not a divisor of 3208)
3208 / 3208 = 1 (the remainder is 0, so 3208 is a divisor of 3208)

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 3208 (i.e. 56.639209034025). 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 $\frac{N}{d} = D$ )

3208 / 1 = 3208 (the remainder is 0, so 1 and 3208 are divisors of 3208)
3208 / 2 = 1604 (the remainder is 0, so 2 and 1604 are divisors of 3208)
3208 / 3 = 1069.3333333333 (the remainder is 1, so 3 is not a divisor of 3208)
...
3208 / 55 = 58.327272727273 (the remainder is 18, so 55 is not a divisor of 3208)
3208 / 56 = 57.285714285714 (the remainder is 16, so 56 is not a divisor of 3208)