What are the divisors of 6143?

1, 6143

There is a total of 2 positive divisors.
The sum of these divisors is 6144.
The arithmetic mean is 3072.

2 odd divisors

1, 6143

How to compute the divisors of 6143?

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 6143 by each of the numbers from 1 to 6143 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)

6143 / 1 = 6143 (the remainder is 0, so 1 is a divisor of 6143)
6143 / 2 = 3071.5 (the remainder is 1, so 2 is not a divisor of 6143)
6143 / 3 = 2047.6666666667 (the remainder is 2, so 3 is not a divisor of 6143)
...
6143 / 6142 = 1.0001628134158 (the remainder is 1, so 6142 is not a divisor of 6143)
6143 / 6143 = 1 (the remainder is 0, so 6143 is a divisor of 6143)

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 6143 (i.e. 78.377292629945). 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 $\frac{N}{d} = D$ )

6143 / 1 = 6143 (the remainder is 0, so 1 and 6143 are divisors of 6143)
6143 / 2 = 3071.5 (the remainder is 1, so 2 is not a divisor of 6143)
6143 / 3 = 2047.6666666667 (the remainder is 2, so 3 is not a divisor of 6143)
...
6143 / 77 = 79.779220779221 (the remainder is 60, so 77 is not a divisor of 6143)
6143 / 78 = 78.75641025641 (the remainder is 59, so 78 is not a divisor of 6143)