What are the divisors of 3143?

1, 7, 449, 3143

There is a total of 4 positive divisors.
The sum of these divisors is 3600.
The arithmetic mean is 900.

4 odd divisors

1, 7, 449, 3143

How to compute the divisors of 3143?

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 3143 by each of the numbers from 1 to 3143 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)

3143 / 1 = 3143 (the remainder is 0, so 1 is a divisor of 3143)
3143 / 2 = 1571.5 (the remainder is 1, so 2 is not a divisor of 3143)
3143 / 3 = 1047.6666666667 (the remainder is 2, so 3 is not a divisor of 3143)
...
3143 / 3142 = 1.0003182686187 (the remainder is 1, so 3142 is not a divisor of 3143)
3143 / 3143 = 1 (the remainder is 0, so 3143 is a divisor of 3143)

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 3143 (i.e. 56.062465161639). 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 $\frac{N}{d} = D$ )

3143 / 1 = 3143 (the remainder is 0, so 1 and 3143 are divisors of 3143)
3143 / 2 = 1571.5 (the remainder is 1, so 2 is not a divisor of 3143)
3143 / 3 = 1047.6666666667 (the remainder is 2, so 3 is not a divisor of 3143)
...
3143 / 55 = 57.145454545455 (the remainder is 8, so 55 is not a divisor of 3143)
3143 / 56 = 56.125 (the remainder is 7, so 56 is not a divisor of 3143)