What are the divisors of 3443?

1, 11, 313, 3443

There is a total of 4 positive divisors.
The sum of these divisors is 3768.
The arithmetic mean is 942.

4 odd divisors

1, 11, 313, 3443

How to compute the divisors of 3443?

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 3443 by each of the numbers from 1 to 3443 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)

3443 / 1 = 3443 (the remainder is 0, so 1 is a divisor of 3443)
3443 / 2 = 1721.5 (the remainder is 1, so 2 is not a divisor of 3443)
3443 / 3 = 1147.6666666667 (the remainder is 2, so 3 is not a divisor of 3443)
...
3443 / 3442 = 1.0002905287623 (the remainder is 1, so 3442 is not a divisor of 3443)
3443 / 3443 = 1 (the remainder is 0, so 3443 is a divisor of 3443)

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 3443 (i.e. 58.677082408722). 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 $\frac{N}{d} = D$ )

3443 / 1 = 3443 (the remainder is 0, so 1 and 3443 are divisors of 3443)
3443 / 2 = 1721.5 (the remainder is 1, so 2 is not a divisor of 3443)
3443 / 3 = 1147.6666666667 (the remainder is 2, so 3 is not a divisor of 3443)
...
3443 / 57 = 60.40350877193 (the remainder is 23, so 57 is not a divisor of 3443)
3443 / 58 = 59.362068965517 (the remainder is 21, so 58 is not a divisor of 3443)