What are the divisors of 3364?

1, 2, 4, 29, 58, 116, 841, 1682, 3364

There is a total of 9 positive divisors.
The sum of these divisors is 6097.
The arithmetic mean is 677.44444444444.

6 even divisors

2, 4, 58, 116, 1682, 3364

3 odd divisors

1, 29, 841

How to compute the divisors of 3364?

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 3364 by each of the numbers from 1 to 3364 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)

3364 / 1 = 3364 (the remainder is 0, so 1 is a divisor of 3364)
3364 / 2 = 1682 (the remainder is 0, so 2 is a divisor of 3364)
3364 / 3 = 1121.3333333333 (the remainder is 1, so 3 is not a divisor of 3364)
...
3364 / 3363 = 1.0002973535534 (the remainder is 1, so 3363 is not a divisor of 3364)
3364 / 3364 = 1 (the remainder is 0, so 3364 is a divisor of 3364)

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 3364 (i.e. 58). 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 $\frac{N}{d} = D$ )

3364 / 1 = 3364 (the remainder is 0, so 1 and 3364 are divisors of 3364)
3364 / 2 = 1682 (the remainder is 0, so 2 and 1682 are divisors of 3364)
3364 / 3 = 1121.3333333333 (the remainder is 1, so 3 is not a divisor of 3364)
...
3364 / 57 = 59.017543859649 (the remainder is 1, so 57 is not a divisor of 3364)
3364 / 58 = 58 (the remainder is 0, so 58 and 58 are divisors of 3364)