What are the divisors of 2443?

1, 7, 349, 2443

There is a total of 4 positive divisors.
The sum of these divisors is 2800.
The arithmetic mean is 700.

4 odd divisors

1, 7, 349, 2443

How to compute the divisors of 2443?

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 2443 by each of the numbers from 1 to 2443 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)

2443 / 1 = 2443 (the remainder is 0, so 1 is a divisor of 2443)
2443 / 2 = 1221.5 (the remainder is 1, so 2 is not a divisor of 2443)
2443 / 3 = 814.33333333333 (the remainder is 1, so 3 is not a divisor of 2443)
...
2443 / 2442 = 1.0004095004095 (the remainder is 1, so 2442 is not a divisor of 2443)
2443 / 2443 = 1 (the remainder is 0, so 2443 is a divisor of 2443)

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 2443 (i.e. 49.42671342503). 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 $\frac{N}{d} = D$ )

2443 / 1 = 2443 (the remainder is 0, so 1 and 2443 are divisors of 2443)
2443 / 2 = 1221.5 (the remainder is 1, so 2 is not a divisor of 2443)
2443 / 3 = 814.33333333333 (the remainder is 1, so 3 is not a divisor of 2443)
...
2443 / 48 = 50.895833333333 (the remainder is 43, so 48 is not a divisor of 2443)
2443 / 49 = 49.857142857143 (the remainder is 42, so 49 is not a divisor of 2443)