What are the divisors of 3424?

1, 2, 4, 8, 16, 32, 107, 214, 428, 856, 1712, 3424

There is a total of 12 positive divisors.
The sum of these divisors is 6804.
The arithmetic mean is 567.

10 even divisors

2, 4, 8, 16, 32, 214, 428, 856, 1712, 3424

2 odd divisors

1, 107

How to compute the divisors of 3424?

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 3424 by each of the numbers from 1 to 3424 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)

3424 / 1 = 3424 (the remainder is 0, so 1 is a divisor of 3424)
3424 / 2 = 1712 (the remainder is 0, so 2 is a divisor of 3424)
3424 / 3 = 1141.3333333333 (the remainder is 1, so 3 is not a divisor of 3424)
...
3424 / 3423 = 1.0002921413964 (the remainder is 1, so 3423 is not a divisor of 3424)
3424 / 3424 = 1 (the remainder is 0, so 3424 is a divisor of 3424)

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 3424 (i.e. 58.514955353311). 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 $\frac{N}{d} = D$ )

3424 / 1 = 3424 (the remainder is 0, so 1 and 3424 are divisors of 3424)
3424 / 2 = 1712 (the remainder is 0, so 2 and 1712 are divisors of 3424)
3424 / 3 = 1141.3333333333 (the remainder is 1, so 3 is not a divisor of 3424)
...
3424 / 57 = 60.070175438596 (the remainder is 4, so 57 is not a divisor of 3424)
3424 / 58 = 59.034482758621 (the remainder is 2, so 58 is not a divisor of 3424)