What are the divisors of 4528?

1, 2, 4, 8, 16, 283, 566, 1132, 2264, 4528

There is a total of 10 positive divisors.
The sum of these divisors is 8804.
The arithmetic mean is 880.4.

8 even divisors

2, 4, 8, 16, 566, 1132, 2264, 4528

2 odd divisors

1, 283

How to compute the divisors of 4528?

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 4528 by each of the numbers from 1 to 4528 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)

4528 / 1 = 4528 (the remainder is 0, so 1 is a divisor of 4528)
4528 / 2 = 2264 (the remainder is 0, so 2 is a divisor of 4528)
4528 / 3 = 1509.3333333333 (the remainder is 1, so 3 is not a divisor of 4528)
...
4528 / 4527 = 1.0002208968412 (the remainder is 1, so 4527 is not a divisor of 4528)
4528 / 4528 = 1 (the remainder is 0, so 4528 is a divisor of 4528)

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 4528 (i.e. 67.290415365043). 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 $\frac{N}{d} = D$ )

4528 / 1 = 4528 (the remainder is 0, so 1 and 4528 are divisors of 4528)
4528 / 2 = 2264 (the remainder is 0, so 2 and 2264 are divisors of 4528)
4528 / 3 = 1509.3333333333 (the remainder is 1, so 3 is not a divisor of 4528)
...
4528 / 66 = 68.606060606061 (the remainder is 40, so 66 is not a divisor of 4528)
4528 / 67 = 67.582089552239 (the remainder is 39, so 67 is not a divisor of 4528)