What are the divisors of 4366?

1, 2, 37, 59, 74, 118, 2183, 4366

There is a total of 8 positive divisors.
The sum of these divisors is 6840.
The arithmetic mean is 855.

4 even divisors

2, 74, 118, 4366

4 odd divisors

1, 37, 59, 2183

How to compute the divisors of 4366?

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 4366 by each of the numbers from 1 to 4366 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)

4366 / 1 = 4366 (the remainder is 0, so 1 is a divisor of 4366)
4366 / 2 = 2183 (the remainder is 0, so 2 is a divisor of 4366)
4366 / 3 = 1455.3333333333 (the remainder is 1, so 3 is not a divisor of 4366)
...
4366 / 4365 = 1.0002290950745 (the remainder is 1, so 4365 is not a divisor of 4366)
4366 / 4366 = 1 (the remainder is 0, so 4366 is a divisor of 4366)

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 4366 (i.e. 66.075714146727). 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 $\frac{N}{d} = D$ )

4366 / 1 = 4366 (the remainder is 0, so 1 and 4366 are divisors of 4366)
4366 / 2 = 2183 (the remainder is 0, so 2 and 2183 are divisors of 4366)
4366 / 3 = 1455.3333333333 (the remainder is 1, so 3 is not a divisor of 4366)
...
4366 / 65 = 67.169230769231 (the remainder is 11, so 65 is not a divisor of 4366)
4366 / 66 = 66.151515151515 (the remainder is 10, so 66 is not a divisor of 4366)