What are the divisors of 4266?

1, 2, 3, 6, 9, 18, 27, 54, 79, 158, 237, 474, 711, 1422, 2133, 4266

There is a total of 16 positive divisors.
The sum of these divisors is 9600.
The arithmetic mean is 600.

8 even divisors

2, 6, 18, 54, 158, 474, 1422, 4266

8 odd divisors

1, 3, 9, 27, 79, 237, 711, 2133

How to compute the divisors of 4266?

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 4266 by each of the numbers from 1 to 4266 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)

4266 / 1 = 4266 (the remainder is 0, so 1 is a divisor of 4266)
4266 / 2 = 2133 (the remainder is 0, so 2 is a divisor of 4266)
4266 / 3 = 1422 (the remainder is 0, so 3 is a divisor of 4266)
...
4266 / 4265 = 1.0002344665885 (the remainder is 1, so 4265 is not a divisor of 4266)
4266 / 4266 = 1 (the remainder is 0, so 4266 is a divisor of 4266)

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 4266 (i.e. 65.314623171232). 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 $\frac{N}{d} = D$ )

4266 / 1 = 4266 (the remainder is 0, so 1 and 4266 are divisors of 4266)
4266 / 2 = 2133 (the remainder is 0, so 2 and 2133 are divisors of 4266)
4266 / 3 = 1422 (the remainder is 0, so 3 and 1422 are divisors of 4266)
...
4266 / 64 = 66.65625 (the remainder is 42, so 64 is not a divisor of 4266)
4266 / 65 = 65.630769230769 (the remainder is 41, so 65 is not a divisor of 4266)