What are the divisors of 4318?

1, 2, 17, 34, 127, 254, 2159, 4318

There is a total of 8 positive divisors.
The sum of these divisors is 6912.
The arithmetic mean is 864.

4 even divisors

2, 34, 254, 4318

4 odd divisors

1, 17, 127, 2159

How to compute the divisors of 4318?

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 4318 by each of the numbers from 1 to 4318 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)

4318 / 1 = 4318 (the remainder is 0, so 1 is a divisor of 4318)
4318 / 2 = 2159 (the remainder is 0, so 2 is a divisor of 4318)
4318 / 3 = 1439.3333333333 (the remainder is 1, so 3 is not a divisor of 4318)
...
4318 / 4317 = 1.0002316423442 (the remainder is 1, so 4317 is not a divisor of 4318)
4318 / 4318 = 1 (the remainder is 0, so 4318 is a divisor of 4318)

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 4318 (i.e. 65.711490623787). 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 $\frac{N}{d} = D$ )

4318 / 1 = 4318 (the remainder is 0, so 1 and 4318 are divisors of 4318)
4318 / 2 = 2159 (the remainder is 0, so 2 and 2159 are divisors of 4318)
4318 / 3 = 1439.3333333333 (the remainder is 1, so 3 is not a divisor of 4318)
...
4318 / 64 = 67.46875 (the remainder is 30, so 64 is not a divisor of 4318)
4318 / 65 = 66.430769230769 (the remainder is 28, so 65 is not a divisor of 4318)