What are the divisors of 4552?

1, 2, 4, 8, 569, 1138, 2276, 4552

There is a total of 8 positive divisors.
The sum of these divisors is 8550.
The arithmetic mean is 1068.75.

6 even divisors

2, 4, 8, 1138, 2276, 4552

2 odd divisors

1, 569

How to compute the divisors of 4552?

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 4552 by each of the numbers from 1 to 4552 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)

4552 / 1 = 4552 (the remainder is 0, so 1 is a divisor of 4552)
4552 / 2 = 2276 (the remainder is 0, so 2 is a divisor of 4552)
4552 / 3 = 1517.3333333333 (the remainder is 1, so 3 is not a divisor of 4552)
...
4552 / 4551 = 1.000219731927 (the remainder is 1, so 4551 is not a divisor of 4552)
4552 / 4552 = 1 (the remainder is 0, so 4552 is a divisor of 4552)

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 4552 (i.e. 67.468511173732). 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 $\frac{N}{d} = D$ )

4552 / 1 = 4552 (the remainder is 0, so 1 and 4552 are divisors of 4552)
4552 / 2 = 2276 (the remainder is 0, so 2 and 2276 are divisors of 4552)
4552 / 3 = 1517.3333333333 (the remainder is 1, so 3 is not a divisor of 4552)
...
4552 / 66 = 68.969696969697 (the remainder is 64, so 66 is not a divisor of 4552)
4552 / 67 = 67.940298507463 (the remainder is 63, so 67 is not a divisor of 4552)