What are the divisors of 4532?

1, 2, 4, 11, 22, 44, 103, 206, 412, 1133, 2266, 4532

There is a total of 12 positive divisors.
The sum of these divisors is 8736.
The arithmetic mean is 728.

8 even divisors

2, 4, 22, 44, 206, 412, 2266, 4532

4 odd divisors

1, 11, 103, 1133

How to compute the divisors of 4532?

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 4532 by each of the numbers from 1 to 4532 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)

4532 / 1 = 4532 (the remainder is 0, so 1 is a divisor of 4532)
4532 / 2 = 2266 (the remainder is 0, so 2 is a divisor of 4532)
4532 / 3 = 1510.6666666667 (the remainder is 2, so 3 is not a divisor of 4532)
...
4532 / 4531 = 1.0002207018318 (the remainder is 1, so 4531 is not a divisor of 4532)
4532 / 4532 = 1 (the remainder is 0, so 4532 is a divisor of 4532)

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 4532 (i.e. 67.320130718827). 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 $\frac{N}{d} = D$ )

4532 / 1 = 4532 (the remainder is 0, so 1 and 4532 are divisors of 4532)
4532 / 2 = 2266 (the remainder is 0, so 2 and 2266 are divisors of 4532)
4532 / 3 = 1510.6666666667 (the remainder is 2, so 3 is not a divisor of 4532)
...
4532 / 66 = 68.666666666667 (the remainder is 44, so 66 is not a divisor of 4532)
4532 / 67 = 67.641791044776 (the remainder is 43, so 67 is not a divisor of 4532)