What are the divisors of 4239?

1, 3, 9, 27, 157, 471, 1413, 4239

There is a total of 8 positive divisors.
The sum of these divisors is 6320.
The arithmetic mean is 790.

8 odd divisors

1, 3, 9, 27, 157, 471, 1413, 4239

How to compute the divisors of 4239?

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 4239 by each of the numbers from 1 to 4239 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)

4239 / 1 = 4239 (the remainder is 0, so 1 is a divisor of 4239)
4239 / 2 = 2119.5 (the remainder is 1, so 2 is not a divisor of 4239)
4239 / 3 = 1413 (the remainder is 0, so 3 is a divisor of 4239)
...
4239 / 4238 = 1.0002359603587 (the remainder is 1, so 4238 is not a divisor of 4239)
4239 / 4239 = 1 (the remainder is 0, so 4239 is a divisor of 4239)

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 4239 (i.e. 65.107603242632). 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 $\frac{N}{d} = D$ )

4239 / 1 = 4239 (the remainder is 0, so 1 and 4239 are divisors of 4239)
4239 / 2 = 2119.5 (the remainder is 1, so 2 is not a divisor of 4239)
4239 / 3 = 1413 (the remainder is 0, so 3 and 1413 are divisors of 4239)
...
4239 / 64 = 66.234375 (the remainder is 15, so 64 is not a divisor of 4239)
4239 / 65 = 65.215384615385 (the remainder is 14, so 65 is not a divisor of 4239)