What are the divisors of 4386?

1, 2, 3, 6, 17, 34, 43, 51, 86, 102, 129, 258, 731, 1462, 2193, 4386

There is a total of 16 positive divisors.
The sum of these divisors is 9504.
The arithmetic mean is 594.

8 even divisors

2, 6, 34, 86, 102, 258, 1462, 4386

8 odd divisors

1, 3, 17, 43, 51, 129, 731, 2193

How to compute the divisors of 4386?

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 4386 by each of the numbers from 1 to 4386 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)

4386 / 1 = 4386 (the remainder is 0, so 1 is a divisor of 4386)
4386 / 2 = 2193 (the remainder is 0, so 2 is a divisor of 4386)
4386 / 3 = 1462 (the remainder is 0, so 3 is a divisor of 4386)
...
4386 / 4385 = 1.000228050171 (the remainder is 1, so 4385 is not a divisor of 4386)
4386 / 4386 = 1 (the remainder is 0, so 4386 is a divisor of 4386)

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 4386 (i.e. 66.226882759194). 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 $\frac{N}{d} = D$ )

4386 / 1 = 4386 (the remainder is 0, so 1 and 4386 are divisors of 4386)
4386 / 2 = 2193 (the remainder is 0, so 2 and 2193 are divisors of 4386)
4386 / 3 = 1462 (the remainder is 0, so 3 and 1462 are divisors of 4386)
...
4386 / 65 = 67.476923076923 (the remainder is 31, so 65 is not a divisor of 4386)
4386 / 66 = 66.454545454545 (the remainder is 30, so 66 is not a divisor of 4386)