What are the divisors of 3344?

1, 2, 4, 8, 11, 16, 19, 22, 38, 44, 76, 88, 152, 176, 209, 304, 418, 836, 1672, 3344

There is a total of 20 positive divisors.
The sum of these divisors is 7440.
The arithmetic mean is 372.

16 even divisors

2, 4, 8, 16, 22, 38, 44, 76, 88, 152, 176, 304, 418, 836, 1672, 3344

4 odd divisors

1, 11, 19, 209

How to compute the divisors of 3344?

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 3344 by each of the numbers from 1 to 3344 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)

3344 / 1 = 3344 (the remainder is 0, so 1 is a divisor of 3344)
3344 / 2 = 1672 (the remainder is 0, so 2 is a divisor of 3344)
3344 / 3 = 1114.6666666667 (the remainder is 2, so 3 is not a divisor of 3344)
...
3344 / 3343 = 1.0002991325157 (the remainder is 1, so 3343 is not a divisor of 3344)
3344 / 3344 = 1 (the remainder is 0, so 3344 is a divisor of 3344)

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 3344 (i.e. 57.827329179204). 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 $\frac{N}{d} = D$ )

3344 / 1 = 3344 (the remainder is 0, so 1 and 3344 are divisors of 3344)
3344 / 2 = 1672 (the remainder is 0, so 2 and 1672 are divisors of 3344)
3344 / 3 = 1114.6666666667 (the remainder is 2, so 3 is not a divisor of 3344)
...
3344 / 56 = 59.714285714286 (the remainder is 40, so 56 is not a divisor of 3344)
3344 / 57 = 58.666666666667 (the remainder is 38, so 57 is not a divisor of 3344)