What are the divisors of 3367?

1, 7, 13, 37, 91, 259, 481, 3367

There is a total of 8 positive divisors.
The sum of these divisors is 4256.
The arithmetic mean is 532.

8 odd divisors

1, 7, 13, 37, 91, 259, 481, 3367

How to compute the divisors of 3367?

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 3367 by each of the numbers from 1 to 3367 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)

3367 / 1 = 3367 (the remainder is 0, so 1 is a divisor of 3367)
3367 / 2 = 1683.5 (the remainder is 1, so 2 is not a divisor of 3367)
3367 / 3 = 1122.3333333333 (the remainder is 1, so 3 is not a divisor of 3367)
...
3367 / 3366 = 1.0002970885324 (the remainder is 1, so 3366 is not a divisor of 3367)
3367 / 3367 = 1 (the remainder is 0, so 3367 is a divisor of 3367)

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 3367 (i.e. 58.025856305616). 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 $\frac{N}{d} = D$ )

3367 / 1 = 3367 (the remainder is 0, so 1 and 3367 are divisors of 3367)
3367 / 2 = 1683.5 (the remainder is 1, so 2 is not a divisor of 3367)
3367 / 3 = 1122.3333333333 (the remainder is 1, so 3 is not a divisor of 3367)
...
3367 / 57 = 59.070175438596 (the remainder is 4, so 57 is not a divisor of 3367)
3367 / 58 = 58.051724137931 (the remainder is 3, so 58 is not a divisor of 3367)