What are the divisors of 4538?

1, 2, 2269, 4538

There is a total of 4 positive divisors.
The sum of these divisors is 6810.
The arithmetic mean is 1702.5.

2 even divisors

2, 4538

2 odd divisors

1, 2269

How to compute the divisors of 4538?

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 4538 by each of the numbers from 1 to 4538 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)

4538 / 1 = 4538 (the remainder is 0, so 1 is a divisor of 4538)
4538 / 2 = 2269 (the remainder is 0, so 2 is a divisor of 4538)
4538 / 3 = 1512.6666666667 (the remainder is 2, so 3 is not a divisor of 4538)
...
4538 / 4537 = 1.0002204099625 (the remainder is 1, so 4537 is not a divisor of 4538)
4538 / 4538 = 1 (the remainder is 0, so 4538 is a divisor of 4538)

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 4538 (i.e. 67.364679172397). 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 $\frac{N}{d} = D$ )

4538 / 1 = 4538 (the remainder is 0, so 1 and 4538 are divisors of 4538)
4538 / 2 = 2269 (the remainder is 0, so 2 and 2269 are divisors of 4538)
4538 / 3 = 1512.6666666667 (the remainder is 2, so 3 is not a divisor of 4538)
...
4538 / 66 = 68.757575757576 (the remainder is 50, so 66 is not a divisor of 4538)
4538 / 67 = 67.731343283582 (the remainder is 49, so 67 is not a divisor of 4538)