What are the divisors of 4254?

1, 2, 3, 6, 709, 1418, 2127, 4254

There is a total of 8 positive divisors.
The sum of these divisors is 8520.
The arithmetic mean is 1065.

4 even divisors

2, 6, 1418, 4254

4 odd divisors

1, 3, 709, 2127

How to compute the divisors of 4254?

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 4254 by each of the numbers from 1 to 4254 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)

4254 / 1 = 4254 (the remainder is 0, so 1 is a divisor of 4254)
4254 / 2 = 2127 (the remainder is 0, so 2 is a divisor of 4254)
4254 / 3 = 1418 (the remainder is 0, so 3 is a divisor of 4254)
...
4254 / 4253 = 1.0002351281448 (the remainder is 1, so 4253 is not a divisor of 4254)
4254 / 4254 = 1 (the remainder is 0, so 4254 is a divisor of 4254)

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 4254 (i.e. 65.222695436481). 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 $\frac{N}{d} = D$ )

4254 / 1 = 4254 (the remainder is 0, so 1 and 4254 are divisors of 4254)
4254 / 2 = 2127 (the remainder is 0, so 2 and 2127 are divisors of 4254)
4254 / 3 = 1418 (the remainder is 0, so 3 and 1418 are divisors of 4254)
...
4254 / 64 = 66.46875 (the remainder is 30, so 64 is not a divisor of 4254)
4254 / 65 = 65.446153846154 (the remainder is 29, so 65 is not a divisor of 4254)