What are the divisors of 4458?

1, 2, 3, 6, 743, 1486, 2229, 4458

There is a total of 8 positive divisors.
The sum of these divisors is 8928.
The arithmetic mean is 1116.

4 even divisors

2, 6, 1486, 4458

4 odd divisors

1, 3, 743, 2229

How to compute the divisors of 4458?

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 4458 by each of the numbers from 1 to 4458 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)

4458 / 1 = 4458 (the remainder is 0, so 1 is a divisor of 4458)
4458 / 2 = 2229 (the remainder is 0, so 2 is a divisor of 4458)
4458 / 3 = 1486 (the remainder is 0, so 3 is a divisor of 4458)
...
4458 / 4457 = 1.0002243661656 (the remainder is 1, so 4457 is not a divisor of 4458)
4458 / 4458 = 1 (the remainder is 0, so 4458 is a divisor of 4458)

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 4458 (i.e. 66.768255930494). 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 $\frac{N}{d} = D$ )

4458 / 1 = 4458 (the remainder is 0, so 1 and 4458 are divisors of 4458)
4458 / 2 = 2229 (the remainder is 0, so 2 and 2229 are divisors of 4458)
4458 / 3 = 1486 (the remainder is 0, so 3 and 1486 are divisors of 4458)
...
4458 / 65 = 68.584615384615 (the remainder is 38, so 65 is not a divisor of 4458)
4458 / 66 = 67.545454545455 (the remainder is 36, so 66 is not a divisor of 4458)