What are the divisors of 3043?

1, 17, 179, 3043

There is a total of 4 positive divisors.
The sum of these divisors is 3240.
The arithmetic mean is 810.

4 odd divisors

1, 17, 179, 3043

How to compute the divisors of 3043?

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 3043 by each of the numbers from 1 to 3043 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)

3043 / 1 = 3043 (the remainder is 0, so 1 is a divisor of 3043)
3043 / 2 = 1521.5 (the remainder is 1, so 2 is not a divisor of 3043)
3043 / 3 = 1014.3333333333 (the remainder is 1, so 3 is not a divisor of 3043)
...
3043 / 3042 = 1.000328731098 (the remainder is 1, so 3042 is not a divisor of 3043)
3043 / 3043 = 1 (the remainder is 0, so 3043 is a divisor of 3043)

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 3043 (i.e. 55.163393659201). 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 $\frac{N}{d} = D$ )

3043 / 1 = 3043 (the remainder is 0, so 1 and 3043 are divisors of 3043)
3043 / 2 = 1521.5 (the remainder is 1, so 2 is not a divisor of 3043)
3043 / 3 = 1014.3333333333 (the remainder is 1, so 3 is not a divisor of 3043)
...
3043 / 54 = 56.351851851852 (the remainder is 19, so 54 is not a divisor of 3043)
3043 / 55 = 55.327272727273 (the remainder is 18, so 55 is not a divisor of 3043)