What are the divisors of 3444?

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 41, 42, 82, 84, 123, 164, 246, 287, 492, 574, 861, 1148, 1722, 3444

There is a total of 24 positive divisors.
The sum of these divisors is 9408.
The arithmetic mean is 392.

16 even divisors

2, 4, 6, 12, 14, 28, 42, 82, 84, 164, 246, 492, 574, 1148, 1722, 3444

8 odd divisors

1, 3, 7, 21, 41, 123, 287, 861

How to compute the divisors of 3444?

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 3444 by each of the numbers from 1 to 3444 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)

3444 / 1 = 3444 (the remainder is 0, so 1 is a divisor of 3444)
3444 / 2 = 1722 (the remainder is 0, so 2 is a divisor of 3444)
3444 / 3 = 1148 (the remainder is 0, so 3 is a divisor of 3444)
...
3444 / 3443 = 1.0002904443799 (the remainder is 1, so 3443 is not a divisor of 3444)
3444 / 3444 = 1 (the remainder is 0, so 3444 is a divisor of 3444)

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 3444 (i.e. 58.685603004485). 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 $\frac{N}{d} = D$ )

3444 / 1 = 3444 (the remainder is 0, so 1 and 3444 are divisors of 3444)
3444 / 2 = 1722 (the remainder is 0, so 2 and 1722 are divisors of 3444)
3444 / 3 = 1148 (the remainder is 0, so 3 and 1148 are divisors of 3444)
...
3444 / 57 = 60.421052631579 (the remainder is 24, so 57 is not a divisor of 3444)
3444 / 58 = 59.379310344828 (the remainder is 22, so 58 is not a divisor of 3444)