What are the divisors of 4143?

1, 3, 1381, 4143

There is a total of 4 positive divisors.
The sum of these divisors is 5528.
The arithmetic mean is 1382.

4 odd divisors

1, 3, 1381, 4143

How to compute the divisors of 4143?

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 4143 by each of the numbers from 1 to 4143 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)

4143 / 1 = 4143 (the remainder is 0, so 1 is a divisor of 4143)
4143 / 2 = 2071.5 (the remainder is 1, so 2 is not a divisor of 4143)
4143 / 3 = 1381 (the remainder is 0, so 3 is a divisor of 4143)
...
4143 / 4142 = 1.0002414292612 (the remainder is 1, so 4142 is not a divisor of 4143)
4143 / 4143 = 1 (the remainder is 0, so 4143 is a divisor of 4143)

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 4143 (i.e. 64.366140167016). 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 $\frac{N}{d} = D$ )

4143 / 1 = 4143 (the remainder is 0, so 1 and 4143 are divisors of 4143)
4143 / 2 = 2071.5 (the remainder is 1, so 2 is not a divisor of 4143)
4143 / 3 = 1381 (the remainder is 0, so 3 and 1381 are divisors of 4143)
...
4143 / 63 = 65.761904761905 (the remainder is 48, so 63 is not a divisor of 4143)
4143 / 64 = 64.734375 (the remainder is 47, so 64 is not a divisor of 4143)