What are the divisors of 4468?

1, 2, 4, 1117, 2234, 4468

There is a total of 6 positive divisors.
The sum of these divisors is 7826.
The arithmetic mean is 1304.3333333333.

4 even divisors

2, 4, 2234, 4468

2 odd divisors

1, 1117

How to compute the divisors of 4468?

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 4468 by each of the numbers from 1 to 4468 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)

4468 / 1 = 4468 (the remainder is 0, so 1 is a divisor of 4468)
4468 / 2 = 2234 (the remainder is 0, so 2 is a divisor of 4468)
4468 / 3 = 1489.3333333333 (the remainder is 1, so 3 is not a divisor of 4468)
...
4468 / 4467 = 1.0002238638908 (the remainder is 1, so 4467 is not a divisor of 4468)
4468 / 4468 = 1 (the remainder is 0, so 4468 is a divisor of 4468)

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 4468 (i.e. 66.843099868274). 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 $\frac{N}{d} = D$ )

4468 / 1 = 4468 (the remainder is 0, so 1 and 4468 are divisors of 4468)
4468 / 2 = 2234 (the remainder is 0, so 2 and 2234 are divisors of 4468)
4468 / 3 = 1489.3333333333 (the remainder is 1, so 3 is not a divisor of 4468)
...
4468 / 65 = 68.738461538462 (the remainder is 48, so 65 is not a divisor of 4468)
4468 / 66 = 67.69696969697 (the remainder is 46, so 66 is not a divisor of 4468)