What are the divisors of 3280?

1, 2, 4, 5, 8, 10, 16, 20, 40, 41, 80, 82, 164, 205, 328, 410, 656, 820, 1640, 3280

There is a total of 20 positive divisors.
The sum of these divisors is 7812.
The arithmetic mean is 390.6.

16 even divisors

2, 4, 8, 10, 16, 20, 40, 80, 82, 164, 328, 410, 656, 820, 1640, 3280

4 odd divisors

1, 5, 41, 205

How to compute the divisors of 3280?

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 3280 by each of the numbers from 1 to 3280 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)

3280 / 1 = 3280 (the remainder is 0, so 1 is a divisor of 3280)
3280 / 2 = 1640 (the remainder is 0, so 2 is a divisor of 3280)
3280 / 3 = 1093.3333333333 (the remainder is 1, so 3 is not a divisor of 3280)
...
3280 / 3279 = 1.0003049710278 (the remainder is 1, so 3279 is not a divisor of 3280)
3280 / 3280 = 1 (the remainder is 0, so 3280 is a divisor of 3280)

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 3280 (i.e. 57.271284253105). 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 $\frac{N}{d} = D$ )

3280 / 1 = 3280 (the remainder is 0, so 1 and 3280 are divisors of 3280)
3280 / 2 = 1640 (the remainder is 0, so 2 and 1640 are divisors of 3280)
3280 / 3 = 1093.3333333333 (the remainder is 1, so 3 is not a divisor of 3280)
...
3280 / 56 = 58.571428571429 (the remainder is 32, so 56 is not a divisor of 3280)
3280 / 57 = 57.543859649123 (the remainder is 31, so 57 is not a divisor of 3280)