What are the divisors of 5143?

1, 37, 139, 5143

There is a total of 4 positive divisors.
The sum of these divisors is 5320.
The arithmetic mean is 1330.

4 odd divisors

1, 37, 139, 5143

How to compute the divisors of 5143?

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 5143 by each of the numbers from 1 to 5143 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)

5143 / 1 = 5143 (the remainder is 0, so 1 is a divisor of 5143)
5143 / 2 = 2571.5 (the remainder is 1, so 2 is not a divisor of 5143)
5143 / 3 = 1714.3333333333 (the remainder is 1, so 3 is not a divisor of 5143)
...
5143 / 5142 = 1.0001944768573 (the remainder is 1, so 5142 is not a divisor of 5143)
5143 / 5143 = 1 (the remainder is 0, so 5143 is a divisor of 5143)

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 5143 (i.e. 71.714712576988). 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 $\frac{N}{d} = D$ )

5143 / 1 = 5143 (the remainder is 0, so 1 and 5143 are divisors of 5143)
5143 / 2 = 2571.5 (the remainder is 1, so 2 is not a divisor of 5143)
5143 / 3 = 1714.3333333333 (the remainder is 1, so 3 is not a divisor of 5143)
...
5143 / 70 = 73.471428571429 (the remainder is 33, so 70 is not a divisor of 5143)
5143 / 71 = 72.43661971831 (the remainder is 31, so 71 is not a divisor of 5143)