What are the divisors of 4534?

1, 2, 2267, 4534

There is a total of 4 positive divisors.
The sum of these divisors is 6804.
The arithmetic mean is 1701.

2 even divisors

2, 4534

2 odd divisors

1, 2267

How to compute the divisors of 4534?

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 4534 by each of the numbers from 1 to 4534 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)

4534 / 1 = 4534 (the remainder is 0, so 1 is a divisor of 4534)
4534 / 2 = 2267 (the remainder is 0, so 2 is a divisor of 4534)
4534 / 3 = 1511.3333333333 (the remainder is 1, so 3 is not a divisor of 4534)
...
4534 / 4533 = 1.0002206044562 (the remainder is 1, so 4533 is not a divisor of 4534)
4534 / 4534 = 1 (the remainder is 0, so 4534 is a divisor of 4534)

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 4534 (i.e. 67.33498347813). 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 $\frac{N}{d} = D$ )

4534 / 1 = 4534 (the remainder is 0, so 1 and 4534 are divisors of 4534)
4534 / 2 = 2267 (the remainder is 0, so 2 and 2267 are divisors of 4534)
4534 / 3 = 1511.3333333333 (the remainder is 1, so 3 is not a divisor of 4534)
...
4534 / 66 = 68.69696969697 (the remainder is 46, so 66 is not a divisor of 4534)
4534 / 67 = 67.671641791045 (the remainder is 45, so 67 is not a divisor of 4534)