What are the divisors of 3397?

1, 43, 79, 3397

There is a total of 4 positive divisors.
The sum of these divisors is 3520.
The arithmetic mean is 880.

4 odd divisors

1, 43, 79, 3397

How to compute the divisors of 3397?

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 3397 by each of the numbers from 1 to 3397 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)

3397 / 1 = 3397 (the remainder is 0, so 1 is a divisor of 3397)
3397 / 2 = 1698.5 (the remainder is 1, so 2 is not a divisor of 3397)
3397 / 3 = 1132.3333333333 (the remainder is 1, so 3 is not a divisor of 3397)
...
3397 / 3396 = 1.0002944640754 (the remainder is 1, so 3396 is not a divisor of 3397)
3397 / 3397 = 1 (the remainder is 0, so 3397 is a divisor of 3397)

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 3397 (i.e. 58.283788483591). 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 $\frac{N}{d} = D$ )

3397 / 1 = 3397 (the remainder is 0, so 1 and 3397 are divisors of 3397)
3397 / 2 = 1698.5 (the remainder is 1, so 2 is not a divisor of 3397)
3397 / 3 = 1132.3333333333 (the remainder is 1, so 3 is not a divisor of 3397)
...
3397 / 57 = 59.59649122807 (the remainder is 34, so 57 is not a divisor of 3397)
3397 / 58 = 58.568965517241 (the remainder is 33, so 58 is not a divisor of 3397)